Sets relations and functions. So let me start with the first part, which is sets Okay You all have done sets before right? This is not a new chapter to us Correct. What do you understand from a set anybody? Jacob Prisha Tanishka Veda, what do you understand from a set? Collection of things absolutely basically set is a well-defined This term is very important. It's a well-defined collection or Aggregate of objects collection slash aggregate aggregate of objects Okay Which we call as the elements of the sets Okay, so objects are called as the elements or members of the set Elements or the members of the sets Okay, now this word well-defined is very important. What do you mean by well-defined? What do you send from well-defined any idea? What are the meaning of well-defined? Sorry, I didn't hear you. What was it? Explicit data. Okay, so it should be clear without any doubt that Particular members should fall to that set or not for example so far set right They normally come in a set of three and two two single single right But they are designed in such a way with respect to their color of fabric and I know Construction that you can figure out that this particular set is a part of this so-called set Okay, or probably cutlery set right you can easily figure out that this spoon or this plate or this cup comes from this Cutlery set and not the other one Okay, if there is any ambiguity Then probably we will not call this as a set Okay, now let me give you some examples where you may feel that there is an ambiguity for example If I say set of all intelligent students in your class Will you call this as a set? Will you call this as a set? No, no because there's an ambiguity. What what what makes them intelligent, right? Intelligent is a very subjective term right or a set of all you can say a dangerous animals Now what do you call dangerous animals even sometimes your pet can also attack right sometimes even dogs But dogs can also attack but pet cats may also bite So dangerous is again a very very subjective term right, but something like this set of all states in India It's well defined right you cannot and there's no ambiguity about a particular state being a state or not a state Okay, so it is completely well defined Okay, but in case where you have you know some ambiguity Let's say set of all planets where life exists So there's an ambiguity in that because we don't know whether there are some planets or Whether you know the planets you have included in your list definitely have life in them or not unless until it has been established Okay, so giving you some examples of sets Let me say a Collection of all vowels right so collection of all vowels in English in English. So this is a set Okay, you can say All colors in rainbow Collection of all colors in rainbow. That's a set Okay, so you may get us in a question in your school as one marker Which of the following is not a set which of the following is a set like that kind of kind of questions can come in your exam. I Can also give you like roots of the equation X square minus 2x minus 3 equal to 0 Okay, so you have two roots coming out of it, which is 3 and minus 1 so you can have a set out of that also Okay, so these are some examples of well-defined. You can say well-defined Collection of objects. So at the same time, let me give you some examples of not well-defined collection, so Example of Not a set Not a set You can say Collection of all big cities in India Now, how do you define a big? You should mention a you know particular area. Okay big is a very, very subjective term Okay, or renowned scientist Renowned scientists of this world Okay, what is the noun? Renowned is not well-defined. Okay, so how do you define a renown? Right famous one or an infamous one. Okay Famous one or an infamous one. Okay, so we cannot claim this to be said because these terms that you see they make it Very ambiguous. They're very doubtful. We cannot talk about them being very well-defined You can say all beautiful all beautiful You know beauty pageants Okay Okay, so What is beautiful? What is not beautiful is all in the eyes of the beholder, right? So we cannot know claims as things to be defined Okay, so these are examples of collection of objects which cannot be called as a set which cannot be called as a set Any questions on this? Now coming to the representation of set Coming to the representation of set. So please Make sure the session is very interactive. Okay. Now you're not in a class of 2025 students. You're only in the class of four four students So make sure you are, you know communicating with me No, you can stop typing. You can just speak speak about it to me. So no need to You know hold yourself back from asking any questions normally a Set is denoted by a capital letter Okay, a b cd is what we use for writing a set. Okay, so this is set is named as a capital letter Okay, so name of a set is written with a capital letter Please do not write small letters while naming up while naming a set Okay, and yes, there are two forms in which we represent it So we represent a set in two forms one is called the tabular form Okay, or we also call it as the roaster form Okay, a roaster form Just like we make roasters right name of the people who will be doing a certain kind of work So that is called the roaster form. Okay, we'll talk about it in some time The other form is basically called the set builder form Set builder form Set builder form Also called as the The rule form where you mention a set by no defining the characteristic of its elements Okay, or defining the rules under which those elements are generated Okay, so that will be covered under set builder form. So let me give you an idea of each one of them separately What is a tabular form tabular form or a roaster form is where you List out the elements where you list out the elements of The given set okay within curly brackets But remember this listing has to be done only once for each element Okay, for example, for example, let's say if I ask you write down the Write down the Alphabet's or write down the set of alphabets that you have in the word mathematics. Okay, so when you have a word mathematics and We are expressing it in the form of a rooster form or a tabular form. We will mention it like this M see how many m's are there that two m's right, but we'll only mention it once In a set every element is mentioned only once Right, please do not mention it more than once Okay, so even though we have two a's will only mention one a okay, even though we have two t's will only mention one t So there's one h one e one i one c one s So if I say give me the set of alphabets in the word mathematics This is how you list them down and this is called Representing them as a roaster form. Okay or tabular form Another important thing about roaster form is you may switch the position of the elements also You may write them in any order you want them, but don't mention them more than once So this can be written in any order. Let me write it down and written in any order Any Okay, so while you're listing down the elements or members of a set in a roaster form or tabular form Please mention them only once and they can be written in any order While you're mentioning them in set builder form.  Why do we need a set builder form? Wasn't the roaster form sufficient enough? Why did you require a set builder form? See many a times you may not be able to list down the elements of a set completely Okay, and you may need to tell the you know person who is looking at a set What is the pattern under which you are generating those elements? Under that you need to use some kind of a formula or a rule to represent those elements and Therefore the set builder form becomes very important Even in the subsequent chapter of relations, you would be requiring set builder form to basically express the relationship between two different variables Okay, remember you were doing functions in the bridge course, right? So why NX were variables which were related to each other by some relation So we cannot mention every point on that particular relation. We can mention it through a pattern or through a rule Okay, wherever listing becomes you can say Non-feasible or impractical will have to use our set builder form to represent a set so in a set builder form you represent a set by Using this kind of a expression it contains all X such that X has a Property px has a property px Okay, let me give you some example of this for example, if I say Give me a set a which contains all X such that Such that X is n square plus n Where n is a natural number Where n is a natural number? Okay from 1 to 3 From 1 to 3 Okay, so this is an example of a set builder form where you're not listing down the element directly But instead told a rule to the person who is just looking at your given set That this is the rule under which you are developing those elements. So I may ask you to convert this to a roster form Okay, so if you convert this to a roster form Okay, how would you write it simple take one first feed it over here one square plus one what it'll be It will be two Okay, put then two two square plus two that will be six Okay, then put a three three square plus three that will be 12. Okay, so this is the Roaster form and this is the set builder form. This is the roster form and this is the set builder form So one type of question you can expect In your school exam to come is that they may ask you to write Roaster to set builder set builder to roster also Okay, now many people ask me this question sir if they have given in those two form and they ask me a set builder form How am I sure that they have written the set in a particular pattern for example now two six twelve They have written in a particular pattern because two came from one six came from two twelve came from three What is the shuffle it and give you so don't worry about that They'll always list down the elements of the set in such a way that looking at it You will be able to find the pattern out Okay, for example Let's take an exercise on this. Let's take a simple exercise on this So now I'm going to give you certain questions where you need to Convert one form to the other. Okay, very simple exercise will take let's say write down the following So hope you are sitting with your notebook and pen write down the following in Roaster form Write down the following in Roaster form This chapter is very easy you will find it super super easy Let's say there's a set Okay, which contains all such elements t such that now this symbol is for such that Okay, many books will also use a dash for it simple state line So don't get confused. Don't think it is a division symbol division symbol is slightly oblique Okay, so such that can be either be mentioned as colon or it could be mentioned as a straight line Okay, so D contains all elements t such that t cube is equal to t and T belongs to real number. I think you were already introduced to the Symbol for real numbers in our bridge course real numbers. Normally we write it with a double stroke r Why double stroke? Why not a single stroke? Because normally single stroke r is used for the word relations Okay, remember the name of the chapter itself sets relations and functions So in relations, we'll use a single stroke r in real numbers. We'll use a double stroke. Yes So please respond to this everybody Tell me what will be the Roaster form Roaster form for this T cube is equal to T what elements will T contain? Okay, what else only one Eight, how come eight cube is eight It's like solving this equation Yeah, so they have indirectly asked you they've indirectly asked you to solve this equation So, let me just sorry. Let me just write it in the corner over here So they have asked you to solve T cube is equal to T Okay, now one habit I have seen in students Canceling out terms. Okay. Remember in the bridge course. I had explicitly mentioned this Do not cancel out factors from both the sides unless until you are sure it is zero Okay, so how do you solve this in a proper way? Just keep terms on one side like this Let's keep the terms on one side like this Okay, Jacob that answer is not complete Manishka also. Yeah, so When we take common over here, we get this right, so this means this means They are Three possibilities either T could be zero or T square is equal to one if T square is equal to one that means T could be plus or minus one both Okay, so this set will contain three elements Zero one and minus one So you can say this is your set builder form. This is your roster form for the same set Is the idea clear? Okay, let me take one more question on this Write down the roster form for this Set E Which contains all elements x such that x to the power 4 minus 5x square plus 6 is equal to 0 Okay, and and your x is a rational number X is a rational number Have you been sense rationally rational? I think you have already done that in class 10 Rational numbers are those real numbers which can be expressed as P by Q form where P and Q are integers and Q is not equal to 0 or It can be expressed as a Terminating decimal or a non-terminating recurring decimal Right just recalling your rational number definition of class 10. Yes Tell me the roster form for this So this is a symbol for such that So colon is one and straight line is such that okay, then ishka Let's wait for others to answer And one more confusion about these classes are dear students. Let me tell you it will only happen in an online mode Okay Physical class as of now. I don't know. I'm not sure about if it'll if it can happen even if the lockdown is over because See online is always convenient if you are focused Okay, if you are a person who is distracted then online is not a you know mode of learning for you But I'm sure it's a very small group of four of you for little go all the way to five or six So online will be much faster Right and we can also, you know decide in a different timings if at all you have any one of you or most of you have some issues, so it is always Customizable according to your needs Okay, so let's solve this question Again in this question. It is as good as solving this equation itself Okay, so let me take it in the side So for the second question So x to the power four minus five x square plus six equal to zero We all know that if I take x square as y Okay, it is just like a quadratic y square minus five y plus six equal to zero Okay, we know it's factorizable if I'm not mistaken. It is factorizable as two and three Isn't it any questions? Okay, so that means y could be two or y could be three So from this quadratic two roots can come out y equal to two and y equal to three Now when you say y equal to two it means x square is equal to two Okay, and when you say x square is equal to two x could be plus or minus root two X could be plus or minus root two, but this does not belong to rational Please note that these are certs Root two or minus root two they belong to irrational numbers. So these are certs certs are irrational numbers What is the third? So it is basically Basically an operation where you are praising a number to a power which is not exactly a whole number For example root two root three root five root six These are all certs root nine is not a third root nine is a three Okay So even when you have a three you don't get a rational number from this because this will give you x as Plus minus root three which is which does not belong to rational number Okay, so the answer to this is this set will remain an empty set So we'll talk about it in some time. This will remain a empty set So you just write curly brackets without you know writing any element between or you may also refer it to a symbol like this This is a symbol for null set. Okay. We'll talk about them in some time. This is called null set. Okay This is fine any question so far Hope the pace of the class is also suitable. Hope I'm not going too fast Is it fine It's all fine, sir. All fine. Veda Jacob. I haven't I haven't heard of heard from you yet. I want to hear your voice Jacob myself. Yeah Jacob Jacob used to I didn't online in this thing. No, uh, when you in class 10 I used to sir. I used to I remember Pratik sir holding your holding a mobile phone or Now I'll give you some questions where you have to convert from roster form to set builder form. Okay So write the following in set builder form Write the following in set builder form following in set builder form so Simple one. I think by looking at it only you can come to know what is the pattern the pattern the question is The set is one one fourth one ninth one sixteen One by 25 Okay Now let me tell you there may be various ways in which you can express it Okay Don't be like Very particular about this is the way only that I can write it. Don't look at the answer of your friend Thinking that oh his answer is different from mine. You may have your own way of writing it Okay So your teacher will be aware of all those different versions of the answer Okay, sometimes you may feel that prime numbers are also working odd numbers are also working So it all depends upon what strikes you at that point of time. There's nothing like Fixed answer for such kind of a thing. There may be multiple answers for the same concept Okay, so please try this out and Let's see You may speak out if you want anybody Done tanishka Okay, so Anybody would like to share his or her answer with me X says that X is one by x square. No, no, no Okay, see You may write it like this a is a Okay, now many people do this x Such that x is one by n square And n is a natural number line from one to five Okay Absolutely correct. Nothing wrong in this answer. So x such that x is one by n square Okay, n being a natural number n lying for one to five. Okay, this is fine. Another person may do directly this Instead of writing x and all he can directly say one by n square Such that n is a natural number lying between one to five Both are accepted. You don't have to always write an x Okay, so you can directly write down the pattern also You may also write one by x square such that x is a natural number lying between You know one to five Okay, so various ways are there. So you may write x one by x square also directly x square So that x is a natural number lying between lying between one to five Okay, or x is a natural number x is a natural number less than equal to five That is also fine Okay, so so many varieties of the same answer you can write your teacher will not mark it wrong Okay, any one of them will suffice Is this fine? Now here the assumption is we have written it in such a way that the pattern is recognizable Are you getting my point? So this is the question that I normally get from students Sir, how are you sure that they have written it in the same order? Right, okay They may have you know the pattern We would have been something else and they would have shuffled it to get this All those questions come to me but rest for sure Whatever is the order in which they have written down the elements you need to find pattern in them only Well, you would have appeared for NTSC exams, isn't it? NTSC exams under the MAT portion we have these kind of pattern identification Sequence and all so those concepts will be applicable over here. Okay, so let me give you one more Second question Uh, let's say Yeah, let's say A contains 2 by 3 3 by 4 4 by 5 5 by 6 6 by 7 7 by 8 Try this out simple Done easy Should not take you more than 10 seconds also to do this Should we discuss it? Absolutely, absolutely So it is N by you can say it contains all N by N plus one type of elements Where N is a you can say integer whole number Natural number whatever term you want to use N is a let's say I write this time as an integer Okay That integer is also signified by I Okay Where N is In the interval you can say 2 to 7 Or natural number from 2 to 7 anything will work fine Now there are certain ones which are slightly challenging So let's say I give you something like this 1 2 4 7 11 16 Okay How do you do in this case? Now this is slightly on a difficult side Let me see if you are able to crack this 1 2 4 7 11 16 What is the pattern here? Let's see who is able to identify the pattern Okay, then Ishka what is the pattern here? Can you can you write it down? Okay, let me put this chart 5 only to the host Yeah, you need to select my name and then type there Okay You know what is the pattern but you're not able to figure it out How to represent it That's the inner problem that people face every year Okay Now this if you can see Okay, let me just list down these elements So if you see this particular set of numbers The pattern is obvious but we don't know how to actually write it down The pattern is the difference between them As you can see The difference between them is in arithmetic progression Isn't it? I'm assuming everybody here knows arithmetic progression of class 10 APs Anybody who doesn't know arithmetic progression? Everybody knows it Okay Now all of you see here what I'm going to do Let us say Let us say I mean just assume that I'm trying to add them Okay Just assume that I'm trying to add them Okay And this 10 continues And let's say I go to some nth term Okay tn Do you remember your class 10th notation tn represented Your nth term of that particular sequence So let's say this is this This is your tn Okay Let me say that this sum is s Okay As of now Just understand that I'm adding all the terms And I'm adding it till the nth term So if I know the nth term I will be able to use that formula Right I'll be able to use that formula just like I'd use a formula here Okay So my attempt here or my question here or my approach here is to find out The nth term of this sequence So what I'm going to do is All of you listen to this carefully I'm going to write down the same thing one shifted to the right So the same terms I'm just writing one shifted to the right So if I continue doing it The term underneath will be tn-1 And the last term will just You know Come after that So it will just exceed the final point Correct Just subtract it Just subtract it Okay So what is s-s? s-s is 0, right Correct And if there is nothing you can consider as 0 here 0-1 is a 1 2-1 is a 1 4-2 is a 2 7-4 is a 3 11-7 is a 4 5-6 And so on Okay Till you end up getting this term over here And there is a 0 over here you can consider 0-tn will be minus of tn Okay Now let me tell you why I'm doing this Because it will lead to Certain important thing that will help me To solve the question As of now is there any problem in this Any doubt regarding whatever I have done so far I'll repeat the process I wrote down all the numbers And I'm assuming that I'm going till some nth term This is just to Help me to find out the formula of the nth term Then what I did was I added them all I called it as s I wrote the same s One shifted to the right And then I subtracted both of them And this is what I'm sitting Presently at Any questions here No problem? Okay Now let me take a snapshot of this Because I'll be taking it to the next page I don't want to rewrite again The whole thing Let me go to the next page So this was what we had written On the previous page Now all of you please pay attention This term tn I will take it to the other side And here I will have 1 plus 1 plus 2 plus 3 plus 4 Up till tn minus tn minus 1 Now answer this question of mine What do you see here I see An arithmetic progression over here Whose first term is 1 Whose first term is 1 Correct? And whose common difference is also 1 And number of terms How many number of terms are there by the way Who will tell me Think carefully and answer How many number of terms are there Till this step to this step How many terms are there Who will tell me Tanishka Prisha How many terms are there It's undefined See total number of terms from here To here was n So this was n number of terms n terms are here Correct? So I'm asking you If I drop the first guy How many terms will be there n minus 1 terms Yes or no n minus 1 terms will be there Isn't it? Yes Any questions Okay Now do you all know the formula for Sum of n terms of an arithmetic progression What is the formula Who will tell me Unmute yourself and talk n by 2 n by 2 2a Plus n minus 1 into d Wonderful Now let's say you are Facing an arithmetic progression Whose number of terms are n minus 1 First term is 1 So 2 Again n minus 1 will become n minus 2 Correct? Common difference is 1 So what will be the sum now Can I say this 2 and this 2 Will get cancelled off It will be n n minus 1 by 2 Okay Yellow curly bracket We still have to add this 1 So your Tn would be 1 plus n into n minus 1 by 2 Okay So you wanted to know the pattern right The pattern is this This is the pattern Now this is on a Complicated side It may not come to you in your school exams But be prepared for this also Probably they may ask you this After teaching you Sequence and series chapter Because this concept is very much there In your sequence series chapter So probably in your Semester exams of February They may ask you a question like this So keep your Ideas clear about it So you may say that the set a Is made up of 1 plus n n minus 1 by 2 type of elements Such that Your n is the natural number Okay by the way how many terms I had given you 1 2 3 4 5 6 right So n is the natural number Less than equal to 6 Now if you don't trust me you can put The values and check For example if you put 1 over here What do you get When you put n as 1 You get 1 only Isn't it because this term will vanish Correct What do you end when you put 2 When you put 2 You will get 1 plus 2 into 1 by 2 Which is nothing but 2 itself Right as you can see You got these 2 When you put a 3 what do you get Check 1 plus 3 into 2 by 2 So that will be 4 Correct So this is your third term Okay so this is the pattern Which probably will not be very evident to you You need to work out all these things And figure it out Now there are shortcuts to get this But I will not tell them right now to you We will wait for the right chapter to come To discuss this We will also do it by a shortcut later By a shortcut later Any questions so far in conversion From roster form to set builder And set builder to roster I think the idea is pretty clear in your mind Can this question come first? Sorry sorry I am not able to hear you How many marks can this question Come for Okay if you just ask for this question It may come for a 4 marker Okay It may come for a 4 marker not less than that Okay because guessing this is not easy People just looking at it Cannot guess this This requires a bit of working out Normally a 1 marker questions Are those where you can answer with a 1 word Or a 1 line Okay just see the sample paper which I Shared with you, you can also download it from google 1 marker Has to be answered in 1 word or 1 line Okay maximum 2 lines Want this Next we are going to talk about Kines of sets Kines of sets Okay There is one more thing which I wanted To highlight before we go into this This symbol is very important This symbol is A Greek symbol We call this as epsilon Okay It is to be read as This belongs to symbol It represents belongs to Okay this is very important Because many people Are not very clear about this symbol Okay There is one more symbol that you will come across This symbol Okay This symbol is to be read as There exists There exists So if you see this dyslexic E Don't be like thinking like Probably they have written an E in a different way This is a symbol Which is used for their exists Okay So we call this as an existential Quantifier So it is an example of an existential Quantifier Existential quantifier Okay so these are Your terms that we need to just know Okay not a very You know Rocket science term Existential quantifier There is a symbol like this You must be wondering What maths is full of dyslexic people Writing A in a reverse fashion Writing E left to right or something No It is a symbol Which is universally made for For all Okay So if you see this A Which is written in an upside down manner Read it as for all Okay This is also called Universal quantifier Universal quantifier So these are the things that we need to Okay Start applying When we are solving For problems in maths This symbol we all know Implies Okay For certain sets we have also made symbols Like this is real numbers This is for real numbers Okay If you just want to represent positive real number We just put a plus This is for positive real number Positive real number Hope everybody here knows What is real number and all Okay For integers We use sometimes z Many books you will see the z Being written with a double line This is just to Make it different from the Symbol z which is used in complex numbers Okay Many times we use i for it Okay Z is a word which is carried from The Greek word which means Z is a word for counting Okay This is used for integers Okay This means positive integers Positive integers Okay Many times they will also use Such kind of phrase like R They will put a minus some number What does it mean It means all real numbers Excluding this number Okay Curly bracket means all those numbers Will be removed from there For example they will say R minus 1 and 2 What does it mean It means All real numbers But excluding 1 and 2 from there Can you map on Many times they will use this symbol R minus They can use brackets Okay What does it mean It means all real numbers Except all those numbers Which fall between 1 and 2 So if I show this on a real number Line They want you to remove this number So only this part And this part Would be covered under this So 1 and 2 interval is removed So this interval is your 1 to 2 interval that has been Removed Removed So be aware of these symbols I think whole number, natural number You already know What is rational number Q is used for The word quotient It comes from the word quotient Q comes from the word quotient And it stands for rational number It comes from quotient And it stands for rational number Many times for irrational number They will use this Or they will say does not Belong to rational number For example if they say there is a number X Which does not belong to rational number What does it mean They automatically mean Q belongs to Irrational numbers What are irrational numbers What are irrational numbers Numbers which cannot be expressed As a P by Q form Okay As decimals they are Non-terminating, non-recreating in nature For example Pi For example E For example root 2 Root 3, root 5 7 to the power 1 third They are all irrational numbers Let me tell you a funny thing There are more irrational numbers Than rational numbers Okay There are more irrational numbers In fact they are of order Than rational numbers So this is a symbol used for irrational numbers Okay So if I use these symbols please do not get surprised Okay Any questions here Complex number, somebody is asking complex number This is symbol for complex number C with a line in between This is for all complex numbers Complex numbers Okay So I was talking about Kinds of sets So under kinds of sets We will first talk about Null set Also called empty set Empty set is a set which doesn't contain Any elements So we normally represent a null set By just two curly brackets Which doesn't have anything in it Okay Now it doesn't mean zero It's a set which is empty Correct It's your cupboard which doesn't contain anything Correct So your cupboard is an empty set Okay Many times we use the symbol Phi This is to be read as Phi Okay I hope you are aware of those Greek symbols Alpha Beta Gamma Delta What is called? Correct This is called row Okay This is called mu Okay This is called kappa This is called tau This is called phi This is called theta Okay, so these are the symbols that you will be You know coming across in maths Especially theta, alpha, beta and all You will be coming in trigonometry chapter So I will repeat their names If you want me to repeat them This is phi This is tau Okay, you will be using this In your physics chapter When sir is talking about torque For torque he will be using tau This is kappa Okay Alpha, beta, gamma Delta Sigma Sigma This is row This is row This is mu Mu Okay, so we represent A empty set by A Phi symbol Give me some examples of sets which are empty Give me the set builder form Of a set which will not give you anything Remember we had already done an example X to be power 4 Minus 5 X squared plus 6 equal to 0 Where X is a rational number And there was no element in that set So that's an example of a set which is Empty set Can you give me more examples of sets which are empty Any set builder form you tell me Which will give me an answer Which will not contain any element in it I am sure you can think of many Many such examples Just one of you to give me an example Any example Unmute yourself And explain to me a set Such that when I write it in Roster form It doesn't have any element in it X is equal to 2 X is equal to Equal to 2 X equal to 2 X cube is equal to 2 X cube is equal to 2 Okay, so 2 to the power of 1 cube 1 third is an element You want to say some other condition on X Where X is an integer Probably Yes If you just say X cube is equal to 2 There will be an answer for it So your set will contain some element X to the power of 10 is equal to X to the power of 2 X to the power of 10 is equal to X to the power of 2 it will contain No 1 and 0 A set of all X Such that X is between a 1 and 2 Or the 1 and anything And X is a natural number 1 and anything and X is a natural number Yeah, like any number You can put Okay, so you can say X lies between Let's say 1.2 and Let's say 1.8 And X is a natural number Yeah Absolutely correct I can give you so many other examples One other example I can give you is Let's say X contains X is a Value which satisfies 2 X plus Let's say 11 is equal to 3 And X is a natural number Okay, so when you solve this You realize that 2 X plus 11 equal to 3 will give you 2 X as minus 8 So X is minus 4 Which is not Which is not a natural number Which is not a natural number Which is a symbol that you need to Use for saying not belonging to Let me make a Slight change here This means belongs to And this means This means does not belong to By the way, the idea is If you strike something For example, if you strike E That means there does not exist Okay, if you strike this Means it does not imply Okay So use that also whenever You want to explain something Okay, so minus 4 doesn't belong to A natural number so this set will be An empty set This set will be an empty set Okay, any questions here? None Next is singleton set Singleton set What's a singleton set? It's a set which will contain only one element in it Okay So it's a set which has only One element in it And that element may be 0 also It doesn't mean, see many people get confused This is sir Is this a null set? No Even if it has an element 0 You should not call it as a null set Null set means it should not have Anything in it, not even 0 Okay This is a singleton set Singleton set means it has only one element inside it Okay So can you give me some example Of singleton set Give me set builder form Of singleton set For example, set of all Capitals of India Right Set of all, let's say x where x is Capital of India As far as my general knowledge is concerned I know there is only one capital of India Which is New Delhi Okay So this will be a singleton set It will only have New Delhi in it Can you give me some mathematical examples Also Give me a set builder form So that the answer is only one Give me slightly you know Good one Okay So that x square minus 2x Plus 1 is equal to 0 Okay And x belongs to real number You can speak out, don't need to type With a very small batch Yeah, x minus 2 equal to 0 And x is a real number Okay, so you can see that the answer here will only be x equal to 1 Sorry, only x equal to 1 So these are examples of A singleton set Okay Next is Finite set Now in order to finite set In order to understand finite set There is something little prior to that Which is called cardinal number of sets Cardinal Number of sets What is cardinal number of sets Cardinal number of a set Is the number of elements in the set Okay It is represented by N with the set written inside packet Okay For example, if I say Sir, can you redefine it? Yeah, cardinal number of a set is basically I'll write it down over here It gives you the number of elements It gives the number Of elements in that set Elements in the set And it is represented by this symbol So let's say if I have A, E, I, O, U And I say what is the cardinal Number of this set Basically I'm asking you how many Elements are there in this set So you'll say 5 Okay Let me come to finite set What's the finite set Finite set is basically Those sets Whose number of elements Is Fixed or finite You can say that It has a finite value For its cardinal number So cardinal number is a finite value For example, A itself Which I have written here in front of you Set A which is A, E, I, O, U It is a finite set Because the cardinal number Of it is a finite value Getting the point So those are called finite sets Okay Many a times you may write a finite set Like this 2, 4, 6 And dot, dot, dot till let's say You can write it as 100 Okay, this is also a finite set Because even though the number of elements Maybe let's say in the tune of 50 Or 100 or 1000s or millions They are finite in number Okay, so this is a set whose cardinal number You can say is 50 So this is an example of another example Of a finite set Okay But on the other hand If I give you something like this If I give you something like this 2, 4, 6 Dot, dot, dot I don't stop anywhere Then this would become An example of an infinite set Infinite set This would become an example of An infinite set Okay, for an infinite set There is no cardinal number Defined, the cardinal number Will tend to infinity Okay, so Few examples of infinite set That you can claim From your daily use is real numbers Right Real numbers is an infinite set Right, natural numbers Many people will like And with a double Integers Whole numbers They are all infinite set Set of all prime numbers They are infinite set As of now we have not yet concluded that There are limited number of finites So that's an infinite set So for infinite set The cardinal number is not defined It will be Tending to infinity Now there may be There may be infinite sets In terms of intervals So let me talk about that also with you Hope you don't want to copy anything from here Can I just slide To the right side of the board Intervals I am sure you would have been exposed to Intervals to a large extent In our bridge course program So When we are talking about intervals We are really talking about A set of points Whether on real number line Or whether on Natural number Or whether on integers For example, if let's say I say X is a real number And X belongs to 1 to 5 This is an interval Because If you represent this On a real number line You will represent it By all set of points Which lie between 1 and 5 Including 1 And including 5 So yes, this is an example Of an infinite set Because you cannot count the number of elements here There are so many infinite Many real numbers between 1 and 5 So this is a Special type of a set Which we call as intervals We don't call them as set We call them as intervals For a change Anishka has a question So we did this on a graph Where we are plotting a graph for a certain interval of X For a certain interval of X So can you define it again? Yeah, interval is Basically an infinite set Right But still between 2 fixed numbers Okay, so this is an example Where you are having Infinite number of real numbers Between 1 to 5 So we say it's an interval You want a definition Who was that? Anishka, Veda, Prisha Veda, Veda You want a definition of an interval I am not able to hear you Sir, we can't hear you I think the internet was unstable from my side I am extremely sorry What is the definition of it? Sir See, don't understand From definition point of view Because in CVSE we never ask Definition and proofs Just understand it If your set is mentioned As an interval Let's say I write it as an interval 1,5 with bracket What is the meaning of it? The meaning of it is All real numbers which is present Now you may be seeing this as a fixed line But let me tell you in that line There are infinitely many real numbers In fact, we say that between Any 2 real numbers There would be infinitely many real numbers So the intervals are examples of Infinite set Just now we talk about infinite set But infinite sets which are Continuous in nature And as intervals So you can treat this as a definition These you can call it as Continuous infinite sets Okay Now interval also is divided into 2 types One is called close interval And the other will be called as open interval I am sure when we were doing Redefinition of functions We talked about x So we were using something called less than equal to And only less than So let me explain you that also When you write square brackets So let's say I take an example x belongs to 1,5 And you put square brackets Square bracket means This is an interval where This is an interval where 1 and 5 both are included in your Real numbers But if you write something like this x belongs to Round bracket 1 and 5 What does it mean? It means 1 and 5 will not be included So this is what we call as open interval Now you must be asking yourself Where is anything open over here I still see a close bracket It is called open interval Because when we started using these expressions We used this expression for it Like this This also means the same thing This also means the same thing But you will find this notation very rare I have not seen many books using this notation They will use round brackets only So what does round bracket mean? Round bracket means In your real number line You will include all values from 1 to 5 Everything which is between them But not 1 and 5 themselves So we remove that 1 and 5 Either by making a gap like this Or you make holes like this Both are fine Holes means Those values are missing from your Given interval Is this fine? You may have a combination of each one of them also Yes, each bracket has some meaning In maths, please make sure You understand the meaning of these brackets However, for those special functions Which you would have learnt in your bridge course Like GIF function, fractional part function They would mention it specifically That this bracket means this But if you don't mention anything Please note your normal way of interpreting will be applied For example, if I say X square plus X is equal to 0 For all X belonging to 1 to 2 Okay So basically what I am trying to say I am just making a hypothetical scenario Or you can say let's say Greater than 0 Let me use a valid one so that It at least sounds correct So when you are reading this How will you read it? The question setter is saying that This is an inequality which will hold true This symbol means what? For all Correct? Remember the previous page we talked about This symbol For all X which belongs to This symbol is for belongs to Okay And close bracket 1 to 2 means How will you read it? Means all X which is from 1 to 2 Including 1 and 2 as well Okay So this is what the statement is This is how the statement is supposed to be read Are you getting my point? So these are the mathematical symbols Which will be Coming your way when you are dealing with Class 11 maps Now as I was telling That there may be Mix and match of symbols also For example they may say X by X minus 2 is less Than equal to 0 Okay For all X belonging to 1 to 2 What do you How do you read this? All values including 1 But excluding 2 So all values starting from 1 And stopping just before 2 At 1.99999 So in 2 is not included in your interval Okay Prisha I did not understand your question exactly Sir how is each bracket read help means How is each bracket to be read? Okay so you will read this as X belonging to 1,2 Close at 1 Open at 2 This is how you will read it Okay This one you will say it belongs to 1,2 closed If you just say 1,2 close means both Side will be closed If you say 1,5 open That means both side will be open So here you will read 1,2 Close at 1 Open at 2 This is the pronunciation Is this fine? Any questions here? Any questions with respect to Finite set Infinite set Null set Singleton set Any questions here please ask Okay So let me now move on Let me now move on To the concept of Equivalent sets Equivalent sets What is an equivalent set When you say a set A is Equivalent to set B Not a very important concept I don't think so any question will come on this For your information When you say a set is equivalent to another Set B first of all note down the symbol It is a symbol which we use As a you can say Double side arrow just like We use it for a reversible Reaction in chemistry In chemistry you probably use This symbol right Okay so this is The symbol which we use for Equivalent sets so when do we Call two sets as equivalent The definition is If their cardinal number is the same Okay but remember you cannot Use it for an infinite set Okay so you can't set two Infinite sets even though their Number of elements are infinite Each their number of elements are equal I told you in the bridge course two Infinities are not the same So when the number of elements In set A and set B are equal We call them as equivalent sets Simple example I can give you is Let's say A contains 1, 5, 7, 8, 3 Okay and I said B contains A, E, I, O, U Since both of them contains 5, 5 number of elements each They will become equivalent sets Okay nothing big in this Very simple concept Next concept that I want to talk about In the last 20 minutes of the class That's very important Subsets This needs a bit of Understanding because this is Probably important from your school point of view What is a subset? How you define a subset Okay If you say A is a subset Of B Normally we use this in our daily Communication also for example just now I told you in the beginning of the class That applied mathematics is a subset Of the standard mathematics The symbol that we use is A cup kind of a Structure with a dash there In between This is a symbol for saying A is a subset of B Now how do you define a subset? When you say A is a subset of B That means A contains All such elements which also Belong to the set B Okay So when all elements of set A Also belong to that of Set B A will automatically become a subset of B A simple example How could you repeat? If all elements of set A Also belong to set B We say A is a subset of B So this is the definition You can say of a subset So when A is a subset of B This is how we define it A contains all Such that X also belongs to B As an example Let me give you A simple case This is your set B Okay Let's say I write a set like this Then this A will be called As a subset of B Because all elements of A Also are elements of B But not the other way round Right Not all elements of B Are elements of A Okay So A is a subset of B And you can say B is a super set of A B is a super set of A So this is the Terminology that we normally Use B is a super set of A Okay Now what is the symbol for that You may call the symbol to be A is a super set of A like this Okay It's just the same thing written in the reverse order But this is very less used This is more widely used Okay Now my immediate question to you would be How many subsets of B you can form How many subsets of B you can form So how many such sets A you can carve out from B Such that all elements Of A are also Elements of B So the possible number of subsets Let me write it down The possible subsets are Okay You can say one Okay From B I can carve out a set Which only has one in it A singleton set probably Okay It can only have just two in it It can only have just three in it Okay It can only have one and two in it Okay It can only have one three in it It can only have two three in it Right Can I say It can also have All the elements of set B also One two and three Because it is still under this definition So unless this definition is True or violated We can state all the elements also Correct So one two three also can be a Subset of One two three And one more important thing we are missing Is the null set Okay When you don't write anything That also is a subset of any set Okay So null set is basically Subset of All the sets Is a subset of So null set Is a subset of All the sets Including itself Is this fine Now count how many subsets have you written Sorry how many subsets are possible One Two three four Five six seven eight Yes or no Now can anybody of Can anyone of you relate The number of subsets Of elements you have in the Given set B So if set B has three elements The number of subsets Coming out from B are eight in number So can you strike a relationship Between this three and eight Common sense Anyone Sir could you repeat Yeah my question is How is this number of subsets Related to the Cardinal number of set B Two n first one Two n plus one Two n plus one So two n plus one should have Given you the answer as seven In this case but your answer is eight Okay let me take another example Probably from there you will get an idea Let's say Let's say I have a Set X Which has only got five and six Okay how many subsets can you Make from this No Prisha that is also not Let's take more examples Probably the pattern Will be evident from there So yes how many possible subsets How many possible Subsets that's right Five Can I say null set first of all Can I say set with five Can I say set with Six Can I say set with five and six Is there any other possibility Is there any other possibility No So when you had two elements here There are four subsets Coming out of it Now are you able to see the pattern When there were three You got Eight subsets out of it You got eight subsets out of it Now anybody sees the pattern here Now would you like to change your answer Would you like to change your answer Prisha now your n square minus one Fails Okay let me take another example Okay let's say there is a set Called W Which has only got one element Okay how many subsets are possible How many possible subsets are there You will say null And the set with one So you have two subsets Is it two to the power n Right there you go This is what I wanted to give So now for these examples It becomes very evident that Let me write it in a box fashion So that you should never forget this Okay If n is the Cardinal number of a set Cardinal number of a set Okay Then the number of subsets Hope you can understand this symbol It stands for number of subsets From the set will be two to the power Na Okay So whatever is the total number of elements Just raise it to the power of two That will be the total number of subsets Is this fine any questions There will be one question definitely coming in your School exam based on this particular property It's a very important one Please mark it with a star Okay Now Let me finish this over here Out of all the subsets that you have written The set where you had written The Set B itself That is called An improper set Or you can say improper subset Let me write it like this Improper subset Let me say out of these eight subsets Seven of them Are proper subsets And the last one that you have written Is an improper subset So you may call these seven as Proper subsets Proper subsets So what's a proper subset Proper subsets are those subsets Which has got at least one element Less than the original set At least one element Less than a original set That's what I am defining Prisha Proper subsets Are those subsets Which has got At least one element Mark the word At least one element less than the actual subset Actual set That is called a proper subset If your subset is exactly Equal to your given set It will be called as Improper subset So out of Two to the power n subsets One of them will be improper So you can break this up as One improper subset One improper subset And the remaining That is two to the power na-1 As proper subsets So sometimes your teacher may ask you That if a given set has got Five elements How many proper subsets you can make What will your answer be If a given set has Five elements How many proper subsets are there in that set What will your answer be Four If your set has Five elements How many proper subsets are there Nine Nine Just follow this formula Two to the power Five Minus one How much is this 31 Is this fine Any questions here Now remember one thing Let me write this as a Extra point for you Note well Five is an improper subset of itself Why? Because when the set itself is When the set itself is written as a subset It is the improper subset Okay Just like one two three itself when it was Written it was improper subset Isn't it? So when you are just having a null set Then remember null set will be its own subset But that subset will be Improper That's why This particular statement I have written Null set is an Improper subset of itself Please understand this concept Because it is going to be Used in subsequent concepts Like power set and all So Please get this right Right now itself Don't wait for data time to come to ask this We will have more examples Don't worry Let's write down the subsets of Write down the subsets of The set which contains The letters L E O Leo Please do that We just have to mention how many subsets Can be formed or No no no you mention the sets also You mention the subsets also Done? Simple? So what are the subsets? Let's write down the subsets Subsets of A So Null set start with the null set Start with the set having just L E O Then two at a time L E L O E O and L E O Again you can see the count will be 8 only Because the number of elements here are just 3 And this last one will be called as the Improper subset Any questions? Any questions here? Is this fine? Now let me ask you this This is the question which normally Confuses a lot of people So let's say this is your subset This is your set A Which of these two symbol is correct symbol? Both are correct I have given you two Notations Tell me are they both correct? Or only one of them is correct? One of them is correct? Which of them is correct? First one First one is correct Why not second one? Some of you are saying both are correct What do you think? Let me ask Jacob Jacob what do you think? Both are correct or one of them is correct? The first one is correct Oh yeah poll Let's have A and B for it Okay Let's have A and B And this is your B statement Okay By the way there is no response For both of them If you feel both of them you can type it out Okay so two of you think both That's why you have not voted Okay one of you think it's both Okay all right Now here Let me share the result So remember this is a wrong notation The second one is a wrong notation So only first one is correct You can't say A set is a Element of a set Unless until that set Itself involves elements like sets For example in this case L is an element of that set So right way to write it is L is an element of the set But the moment you put this curly bracket Right There is no element like this inside it Can you see any curly bracket L over here No right In this case In the present example Writings B statement would be a blender So this will be wrong So this is the right way to represent it This is a subset you can say of A Are you getting my point This is where people don't realize The difference between The set And difference between element Now if I give you a question like this I'll take another question These are very conceptual questions Your teacher made Ask questions on this If let's say I write it A set which contains L E O Now see what has happened Not only L E O R Elements of this set But a set with L And the set with E O R also elements Are you getting my point Sir can this be considered as a subset No wait Let me ask questions here If I say write down the subsets of this Okay How will you write Let me take a simple example So that you can understand the difference Let me remove out some unwanted things Because it will be very long a problem Let's say I write it like this Okay Now please note I have not repeated Any element These are two elements present in the set So set itself So set itself can be an element of a set Getting my point Right So cupboard may itself contain a cupboard Getting my point So If here if I ask you Is this A subset Of A Or this an element of A You'll say both are correct Both are correct Okay Because You can make a subset out of this element Which will match with this So this can be a subset of A And there is an element like this also Okay so both are correct In this case But let's say if I remove this Let me take a separate example If I say a set contains Only of an element Which is a set itself Correct Then what will you write Will you write this as an Element or a subset of A What will you write Choose will you write this symbol Or will you write this symbol Yes I am still waiting for the response Belongs to a subset Please type it out if you are not able to speak Absurd No my dear It will be belonging to Now this is behaving as an element Let me show you what will be the subsets Subsets will be now set Okay A set containing the Set L which is the set itself Okay Neither of these two is actually this This and this are different Let me tell you These two are different This is a set containing L This is a set containing An element which itself is a set This is where 99% People fail to understand The meaning of a set Are you getting my point So think as if this is a bigger Elmira and this is a smaller Elmira Out of it So if I take out a smaller Elmira and ask you Is this an element Of your bigger Elmira you will say yes Are you getting my point You will not say it is a subset Of it Okay so in this case it will be An element This is not a subset This will be a subset So a set with That element will be a subset of it So these two rotations are correct But here please do not write This is a subset of it No this will be wrong This will be wrong This will not be a subset of it Are you able to get to this point What do I mean by See many people fail To understand that Itself could be a set in itself Okay So when you are representing a subset You have to put double brackets outside it Just like I have done over here Let me take one more question Then only we can close this session One more question Let's say Write the subsets Of Write the Write the Subsets of One Two Let's say TQ Now see here Set A contains three elements This is one element This is another element And this set itself is another element Are you getting my point So think like there is a cupboard Big cupboard A Within that there are two cupboards cupboard B and cupboard C cupboard B has one item inside it cupboard C has got two items inside it And the third item which is two Is outside all the cupboards Okay So it's a situation like this There is a cupboard Within that there is one more cupboard And there is one more bigger cupboard Okay So there is a cupboard which contains one There is a cupboard which contains P and Q And there is an outside element too Okay So this is how basically this particular Set can be perceived So this is an element of the cupboard A This is the element of the cupboard A And this is also an element of the cupboard A Okay So please accept the fact that Sets also can be elements of a Bigger set Now see For example real number Real number itself contains sets of Set of integers itself contains Set of natural numbers Isn't it Okay Now if I ask you to write the subsets What will be the subsets? See the solution Null set The very first subset that you should always write Is the null set Next is now see All of you please watch out here The next set will be a set of One Set of the set one Don't write it just like set one It will be wrong Okay Next would be set of two Next would be Set of two Next would be set of Set of P and Q Correct Next would be set containing one And two Next would be a set containing Two And P and Q set Okay Next would contain the set of One and P and Q And finally will be The whole set itself Which is your improper subset Okay so count How many subsets are there One, two, three Four, five Six, seven Eight Total number should be eight Because there are three elements inside this The power three which is eight Is this clear, any questions here Now you understand Now if I ask you this question Let me put this as a final question Is this an element of A Or is this a subset of A Type it out Yes Concluding questions of the class Is this In this question is one the element Is a set of one is an element of A Or is it a subset of A Jacob has already answered I want everybody to answer All the four of you Tanishka now I'll faint Yeah Do you see this as a subset my dear Hmm This is An element of A Not a subset my dear If I had to write it as a subset I would write it like this This is a subset of A Okay You have already written all your subsets No just check Have you written any subset like this I don't think so If you are confusing it with this Let me tell you it is a different thing This and this are different things Okay Alright so with this we conclude this But one isn't there What is the meaning of one isn't there Is a set of one Not an element of A Look here So that is the answer It is not a subset of A If you had to write it you would have written it like this And this is different These two are different things There is an extra curly bracket outside here There is only one set of Curly brackets Getting it Tanishka Okay so Don't worry I'll be sending this video to you I'll re-watch this video This concept is important Last one don't take it easily that Okay no it's fine Even if I don't understand this no There is a topic called power set There is a subtopic in sets called power set That is coming to you next class When we have Next class would be Of a slightly more duration Two and a half hours is fine Any problem with Two and a half hours It was your first class that's why I thought I would keep it slightly lighter


In today's video we're opening up a Yu-Gi-Oh! collection box with old vintage cards inside. What's up guys we're back with another collection opening. We have some pretty old school cards to show you guys today but before we hop into it we do have giveaway. I'll be giving away these three legendary collection GXC careers that we pulled in a video recently. Just like the video be subscribed turn on notifications let me know down below your favorite card in the collection. I think there's some really awesome ones and hopefully they're in great condition. But before we open it we do have a note. Hey Ruxin it's Logan or Logan on Insta. I just wanted to say congrats on 200k. Been a subscriber since 15k and can't wait to do business with you. I definitely overpacked for 32 cards okay so I remember them being a smaller amount there was a really big box so I didn't know exactly what was going on there but I could never be too sure so at least they're gonna be safe. I mean there's a lot of room for protection I guess. All right so Logan sent us this which is you know obviously a little bit smaller than that box but hey better more room than less room as that what I would always say I mean I don't always say that but now I'll start saying it. Okay I got them out we have their all top litter which seems to be or at least maybe they all are a lot of them are. This is a quality over quantity collection it seems I don't remember exactly what's in here I remember one specific card but if it's a lot like that card then it's gonna be a great collection. Let's see what Logan sent us and what we will be picking up today. Okay so it looks like some of these are not top litter so I guess these are more the low-end cards let's find out so the first card we have is an unlimited magic ruler forceful sentry that's pretty cool we have game promos we have the negate attack from the sacred cards a very classic gba game that basically everyone had if you had a gba oh is that a reverse ring of destruction that is beautiful secret rare looking good there we've got a slate warrior that's from world championships jails and for the game I think that might have been was that game boy as well I didn't have that one we have a flute of summoning dragon that's sdk got unlimited mrl mystical space typhoon we've got sorcerer of dark magic this one is from the movie pack this is when you don't get the blue eye shiny 3200 attacks pretty nice like beast skull monster reincarnation that's a super we've got a nobleman of cross out first ed from pharaoh's servant very cool vampire lord from rise of destiny royal command a little bit of a fade there interesting first ed from l o n beautiful a is that not a reverse imperial order just regular imperial order then we have a revival jam first ed from l o n so pretty nice old school cards there for the most part seems like they're in pretty good condition we're going to be going through the higher end ones and actually checking condition on those though all right so the next one is a harby's feather duster so also from a game boy game the sdd stare at a destined duel let's pull it out check it out see if it's in good condition front looks to be pretty clean on this back does as well this looks like a very clean card might be a couple of small scratches but overall this seems to be a really good condition harby's feather duster all right very cool i mean still a playable card to this day it's at one it's not even a at three because it's so good it was banned for a very long time okay next up so we got some game promo action a lot of old school ooh a dark magician sd y not first ed i mean that would be crazy but unlimited is still very nice if it's in good condition let's look at it the way he's like packaged these makes it seem like he kept good like care of these cards a little bit of a small indent right there but not too much let's see can you see more on there overall it seems to be okay condition i don't know how it would grade with that like slight indent but overall like looks like definitely a new mint card which is beautiful and really hard to find these in your mint most of them are like mod play heavy play damage for the most part because people just played the crap out of these okay next one is a dark magician and this is a little bit different because this is like i'm guessing that this dark magician might have been in the uh what is it the dual masters guide so it was a 2004 print they usually look like this more yellow and then these are the more of the old original 2002 unlimited so they kind of got that darker print i think not a hundred percent sure on that but i'm pretty sure the dual masters guide looked like this the 2004 version and then this was more of the old school originals this is pretty classic let's see how this one looks if it's in the same or similar condition as the other one that one does have a little bit of a bend going on there so that's got a little bend going on back definitely yeah this one's not as good in terms of condition but honestly seeing this just looks amazing these are super pretty cards this dark magician brings back so many memories i mean almost everybody had this card because it was in the starter deck but just seeing it like man such a nice looking card okay what's up next so pretty cool old nostalgic card so far let's see if there's anything huge we have a bpt dark magician okay where's the secret rear going is a reverse no that is a regular secret rear that's fine let's see what kind of condition it's it's bpt so i don't expect too much got some silvering at the top you got a little bit uh yeah back scuffing probably ride out of tin like that for all we know that whenever we open these bpt's that's just how they tend to appear which is still not bad still decent condition what is this buster blade or ferro servant okay no first eds yeah we're looking for i mean we have like revival jam and stuff but none of the big ones have been first ed yet here we go buster blader unlimited definitely an og print definitely not like a 25th or a reprint 2017 definitely got some weird to it though and some scuffing but still a pretty buster blader you love to see those originals the foil shines really nicely in this all right what do we got next will it be a first ed card we have a monster reborn lob so this is a spell card so you can tell immediately this is not a 2002 could be a 2003 print this is when they started doing spell got a little bend to that corner unfortunately oh man it's pretty it's pretty bad but other than that it's really clean it's just that one you know it's pretty significant bend on the corner but otherwise still a really cool looking card this is probably if i had to pinpoint it between 2003 and 2005 print no it's 2003 definitely because 2005 would have en in 2004 as well so this is a 2003 after they changed from magic to spell so could have been from a tin could have not i think the tins usually are magic but sometimes they do have spells well okay not bad we're figuring those out another monster reborn we got a magic card this time see if we can pinpoint this is probably unlimited 2002 oh wow this one definitely has some wear to it definitely a little beat up on this monster reborn yeah little is an understatement definitely unlimited 2002 or same thing 2003 i would guess based on how it looks it's 2002 but uh it could be wrong unfortunately very beat up all right next card is oh a first ed it's invader of the throne why didn't this one get a top loader but revival jam did that's what i'm wondering that is what i'm wondering all right invader of the throne yeah the top's not looking great you can't really see it on the camera actually looks a lot better through the camera than it does live which is interesting it looks almost minty in the camera but on the top i can see how much our corner issues okay but still not bad i mean compared to that monster points things like mint i'm just having fun going through these is what i have to do every time i really should be marking these as i go okay next card is united we stand first edition okay labrador nightmare coming in clutch will this be a minty looking united we stand unfortunately not we got a little bend there oh pretty pretty significant bend goes to the back man that's it that's the only thing the rest of it's clean unfortunately first ed united we stand still a really awesome first ed card a beautiful foiling foiling just hits on these old cards all right let's keep going i know a lot of you guys enjoy these videos they're a little bit more uh slow paced calm so if you are enjoying them make sure to let me know that you want to see more collection purchases like this graceful charity very cool first ed they're all got those bins at the bottom man they're so clean too like these feel like they're old school like from a collection and like they were kept in such great condition minus the bins which it was just hard not to bend stuff back in the day all right so a few cards left what else do we have we have a premat that's a great card premature burial looking strong looking awesome will it have a bin to it i think the corner has a little bit of a bin let's see this corner is the one that's a little bit you can kind of see it in the light that's not too bad though if that's the only thing the rest of the surface looks really clean that corner really is in that bin this is like lightly played maybe like at worst yeah that's really it this card's actually pretty nice all right we're down to like maybe 10 cards a little bit more than that let's find out we have a penguin soldier all right the penguin the soldier got some cards from the starter decks that's pretty classic penguin how you looking uh okay penguin clean uh there is a little corner very slight bend very slight bend but the rest looks pretty good overall not bad definitely uh a very solid condition card one of the best we've seen so far i wouldn't list as near men on tcg just because people would want you know meant for near men so i'd probably put like play but it's really good all right anything else big come on let's see what we can get oh no is this bent can i tell us at the sleeve beast of tau war all right pharaohs servant get some ultras this is what we have not pulled in a long time out of pharaohs servant okay wow this thing seems really glossy for some reason okay okay it's not bad it's all the top corners like not being perfect but this one's definitely pretty decent i would say is a very solid condition old school card for sure a little bit of silvering on the top two but really not bad little small amount of scuffing on the back as well but very cool looking card i mean there's something about this lighting that is just crushing it right now tau war definitely hasn't underrated our work that looks really really good what else we got goblin attack force a lot of pharaohs servant i don't know what could that mean what else will be in here goblin attack force ultra rare it's got a slight bend it's like a little bit of a dent it's like a binder ding i think probably was in a binder at some point you can kind of see it coming through on the back yeah that's unfortunate that happens to a lot of old school cards especially like when back in the day we had no idea about binder dings we didn't really care about condition either all right what is up next we have oh the blue eyes white dragon all right lob not lob i mean sdk i got a little excited there no lob blue eyes that would be cool sdk this is definitely a 2002 i would i would guess definitely i say definitely there's a little bit of a dent right there very cool card looks like it might have a binder ding as well up there i gotta double check that i feel like you can see the name through the back a little bit can you guys see this you can if you catch it in the right light you guys can see that there is a it is coming through the back not super obvious but it is coming through the back the name which is interesting that does happen sometimes on old school cards very interesting to see that i haven't seen that in a while but sdk blue eyes white dragon still really cool okay a few cards left lord of d secret rare we're gonna pick it up a little bit because i'm going a little slow but i'm kind of enjoying this secret rare bpt very nice if you run through this real quick you have mod play yeah with that ding those scuffing on the back beautiful secret 2002 secret reyes were incredible the secret rest from the 10 they just crushed those okay a few cards left will there be something huge in here summon skull from the 10 all right come on give us a minty one if i graded one of these a 10 it would be insane look at that secret rare man that is beautiful wait this one looks a lot better it does have some scratches on the back definitely not perfect it's got that whitening right there this is definitely better than the lord of d the front looks really good i wonder if this came in a blue eyes 10 wink wink anybody remember that yeah yeah that's crazy okay is it a full bpt set let's find out we have oh good start we're our net we're now three out of six right now red eyes black dragon looking good oh man that thing got a nice bend on it yeah this thing is real beat up got some dings on the back some scuffing yeah that thing is it's got a giant dent in the middle unfortunately but still really beautiful card classic secret rare from bpt 2002 i bet it's a bpt set that's what i'm guessing come on oh no it's not okay tune mermaid first ed this is a bad either we can take this tune mermaid i once graded a couple times i grade to piazzett and i think we got a little small thing at the bottom little stuff going on with the corners yeah not bad not bad it's decent tune mermaid mrl first we'll take it all right we're down to three cards left what will be oh jenzo this is the one i knew i knew there was a jenzo in here i don't remember anything else there's still two more cards i guess are they better than jenzo that'd be pretty impressive i don't know what kind of condition this thing's in oh no it's got a ding at the top got a little ding at the top up there it's got a little bend on the corner wow okay but still these are really nice i mean it's beautiful yeah i got some scuffing on the top definitely scuffing on the back oh dint in the middle does it come all the way through i can't really see it on the front but you can definitely see it on the back right there didn't right there so it would be on this side yeah you can see it actually dang still a really awesome first ed pharaoh's servant secret rare so we're not looking at like a lot of minty cards today but we are looking at some very nostalgic these are in a nostalgic condition like they were definitely used or like someone had these in their collection and really enjoyed them which is always really cool to pick up some of those as well it doesn't always have to be like ps810 to be appreciated all right two cards left i don't know what to expect now we have a blue watch from sk e wow okay what a what a wet fart way to end this yeah yeah sk e this is the one that people are always like i have that blue eyes talking about the loby blue eyes and it's just the sk e version yeah these are very cheap even to this day these are not that crazy and they're kind of just like lame because you could get this artwork in loby or in bpc 2002 so it's like this is like the third option and it's a super so it's kind of like eh okay you know not that crazy hopefully we don't end on sye dark magician that would be rough okay okay jmp willy's got a blue eyes jmp is still pretty cool same thing with this one though this could be the game promo version that one looks a little bit better but this one's so cool it does have like the white lightning action shot happening which is pretty cool this one's also pretty clean actually corners a little white but uh oh there we go got some damage at the bottom unfortunately okay so yeah fun collection a lot of old school nostalgic cards hopefully you guys enjoyed it and checking out the conditions if you did make sure to subscribe the channel and uh check it out for more epic content and previous epic content over 1500 videos on the channel so might as well go watch it hey guys i wanted to let you guys know at the end of this video that i did not end up purchasing this collection a couple reasons i wanted to let you know because number one a lot of times people ask me hey do you have this card for sales that available so no it's not a lot of people still ask me and then they'll get to this part they'll say actually i just saw the end of the video yeah it's not available my bad but secondly i wanted to show the video because i went through a lot of the conditions on this collection a lot more than i even usually do it turned out because when i open these up i haven't actually paid for them a lot of the time because we agree send them to me i'll check them out make sure everything looks good and then i'll send you the money so we did that here i checked everything out and i was like okay so then i priced everything out i sent him the price and he didn't agree with the conditions on that i evaluated which is not a big deal the guy's super chill i'm not like insulting him or anything but i ended up just sending it back because a lot of time if you don't agree on condition that the price is going to be so far apart like if i think it's mod play and he thinks it's near mint that's like a very big gap there and there's not really a reason to continue like doing business at that point you should just send it back to him because they think they can get near mint price which i disagree you know i thought that they were more like lower conditions but it seems like he might not have a lot of experience in and chcg here like actual condition because a lot of times people come back with their old collection and i remember doing this myself when i first got back with my old cards or i looked at my old cards for the first time in 2018 i was like man these cards are really nice shape like when i was looking at the price i was looking at near mint price and everything and nowadays i go back and look at them like there's like creases in them and stuff and i thought they were near mint so it can show that like when you're first getting back into it or maybe you're not super well versed or you don't do trading cards a ton you don't really you know mess with the conditions you might not know that like a crease means like it's probably heavily played now because it has a crease in it or if it's like got a slight bend on the corner that can't be near mint or if it's got you know scratches on the back that's gonna drop it down a light place stuff like that so it's just stuff that you wouldn't notice but i wanted to show like me evaluating the cards and then let you guys know that not everybody knows that and a lot of you guys probably don't know about evaluating conditions either because you're either just getting back into it you're new to it you never really paid attention to it maybe you don't even buy cards you just watch the videos so i thought it'd be interesting to show you know some of the cards that we checked out some of the prices that we kind of popped up on the screen and stuff like that and uh just a little bit of an update at the end because i didn't want you guys to think that we bought it and we didn't so it didn't go through no big deal to the guy because he was actually super chill as a fan of the channel so it was cool i'll send it back to him he'll you know do whatever he wants with it i guess he'll try to sell it on his own or whatever he says that other people offered him more so it's like cool perfect you can sell to them it'll go well so uh i figured i'd let you guys know at the end of the video let me know in the comments your experience with like conditioning cards selling stuff buying stuff all that different stuff because there is a lot of nuance when it comes to that kind of stuff so i'll be interested to see you guys stories in the comments and uh thank you guys for watching shout out to home flow show daxer jt chill puffins of doom ornesto dn of miss cycle america doidster supreme stage 21 and under tight show ian moussa junior barding and mimic echo thank you guys for supporting the channel and i'll see you guys in the next one peace


Well, hi there, I'm Sandi Almok, artist and paper crafter here on YouTube, and today I'm going to show you a way of swatching your AI watercolor sets, your art impressions, watercolor sets, and I'm going to show you the 10 new sets they have here early in 2017. For each one of these, I cut a little tag and put a little hole in it so I could put them on a ring. You could also tuck them into the packaging if you keep them that way. A lot of different things you can do. If you have different packaging, you keep them in, like I put all of my containers in one stamping up case, those big flat plastic cases, just make a swatch card of some sort that fits in that and swatch everything that's in it, and that way you have an idea of what those stamps look like because they're cling stamps, they're hard to see sometimes because they're just little gray lobs. And on this, it also gives you practice at doing your watercoloring and gives you an idea of what it can look like in different colors. I'm using Tomo markers for these and a silver brush, which is a number eight round, my kind of go-to for painting anything with, that's going to be on cards, the small things. And I've been using a 12 lately for those wondering what I've been doing in my sketchbook that I've been sharing on Instagram, generally a 12 or above for that. Here I'm adding some color to it, there wasn't enough color in the stamped ink, so you can add things to it by putting a little bit of marker onto a block and add some color to it. I also had added more water than I should have in the first place since some of my lines started going away, so you can repair them after they're a little bit dry. The paper I'm using for these little swatch cards is not the stuff that I normally would use, but I recommend that you might want to do that. I just had some scraps cut as tags, so that's why I decided to use them for this project. This is Kansan XL, the really inexpensive watercolor paper, and I use it sometimes for practice things. I typically tend to like the way that these work on Kansan arches, usually either the rough or the cold press. Just because the edges tend to have more of that watercolor texture, they tend to smooth out too much on a student grade sort of smoother watercolor paper like this. One of the things you'll notice in some of these is that I'm using more water or less water and I'm getting more of an effect or less of an effect, and when I say effect, sometimes that's a good thing and sometimes that's a bad thing. If you use too much water, your lines will all disappear, so you may want to be really careful in how much you add if you're getting really wishy-washy looking images. If they're too dry and they're not moving at all, then add a little bit more water, but have a cloth or a sponge or something off to the side so that you can constantly be working on dabbing off some of your water or adding on some of your water. These are all being painted with the Tombow markers. I have the full set because I'm crazy that way. At the end of this video, I'll show you some comparison with a few other markers. I got some new ones just as I was getting ready to start doing the voiceover for this particular video, so I decided to do a little tiny quick test as my first thing ever with that marker, so you'll see that in just a few moments. Some of the sets, like this one, have a main image that you can put something in, put some flowers in like this wagon, and some just have the containers, some just have the flowers, so it's good to have a mix of different stamp sets, and those of you who are addicts know that I have a lot of them too. Here I'm adding some ground underneath this one. You'll notice on some of the stamps, you can see that black and white picture of the wagon over on the left, they don't finish off the image. That means you're intended to cover that with something.  Different grasses like these, you can add a bunch of water at the bottom to sort of make a clump out of them and make them a background image. Others you can just drop a little bit of water into, and each one of these you can sort of just watch my brush and see how I'm moving the color around to create different effects. With this chair I wanted it to look nice and rustic, and I'm trying to allow a little bit of light and dark. You don't want to put so much water on there that everything starts to disappear and mush, so I'm being a little bit careful about how much water goes on there. This flower I'm just adding a little bit of water in the top flowers, and then you can dab off color as well. When you start making your compilation of a bunch of flowers, you can very easily just remove some color and let the flowers sort of fade into each other, fade into the grasses, that kind of thing. Here on this one I go a little bit too far with it, but I thought I'd show you how you can make a clump of grasses out of just this one grassy bit. So I'm just adding a bunch of water and trying to soften the bottom so I don't have a hard edge, and then making some really soft grasses around it by just flicking that brush around. So you could stamp some flowers on top of that, and then you have this nice green background. You'll notice with this little bit here I'm painting around the little vines so that I can create some laziness. So if you're very careful with your brush you can create some extra detail around each one of the images by just being careful with your water. Just make sure you don't use a whole lot. Less is better if you start having things that mush out and turn into big blobs, and more is better if you want big blobs. Generally the back layer is best off being very soft and light and washy, and there will be a playlist at the end of this video so you can actually go through and see some full paintings done by me, and I will have some examples at the end of this video as well. Some paintings I've done with these stamp sets. There's some flowers where you're just going to put those in the front, like that little single flower might be just one by itself, so I didn't put a whole lot to it. You can also create a little more of a bush like with this one, just with a lot of water down at the base and trying to water out those bottom stems so they don't just end abruptly. Different markers will react differently and different papers will react differently, so you have to test it out for yourself. I can't tell you 100% use this marker, use this paper and you will get this effect. It is like any art, it's practice, practice, practice.  It really is up to you what look you want and whether or not you're putting it in a front layer where the more detail would be or in a background where it would be a little softer. The great thing about these stamps and this whole art impressions watercolor thing is you can do any one of those techniques with it. You can make it soft, you can make it really crisp and hard-edged. Depends entirely on what you would like it to be. You also have these great animal sets now that they're coming out with which is really fun. They've had a few little birds and little rodents and I think there was a bunny in one of the sets but they've kind of slipped in randomly here and there but they've got a couple sets now that are pretty solidly animals and this one is all birds so I would recommend that you go to Google find your favorite bird, stamp it in a color that's going to work with that bird and then try to mimic it and I know there's oddly some people who don't understand that you can actually Google very easily for reference material. Just put in bird standing gray if you want to do a gray bird and you will get so many pictures of standing gray birds. You can get very specific with your Google searches so you can find some reference and follow along. These bunnies are another set that's a lot of fun. They'll be good for Easter but also for any time of year because bunnies can be in spring, in summer. You can use them with fall trees and fall leaves and they would be really cute. You could even put some Christmas gifts around them and let them be part of a Christmas scene, a winter scene, in a forest. A lot of different ways you can use bunnies. There's a lot of stamp sets you might already have that have cute bunny sentiments and that's another thing with these art impressions when they go with your sentiment sets really well because they're just imagery and they're very generic florals for the most part but all different kinds of things too. On my blog there's going to be a giant conglomeration of all of the art impressions, watercolors, sets that Ellen Hudson carries and you know I point to her you can always go to the art impression site as well but I recommend going to Ellen because you're always going to need some cardstock. You're going to need something else and you might as well share your shipping so that is one reason that I try to make sure Ellen is carrying stuff that you need. So here I went in too fast. I went in too soon to add darker color to this bunny so it bled like mad so I've got a dry brush I'm trying to move that color around and not let it be too icky and just sort of made it I just yeah I went overboard to say the least. I'm going to let him dry a bit before I fuss around with him and this little bunny is just the front end of the bunny so you can put him in a container in a wagon in a bucket in whatever you're doing just the front end of him and this little guy decided to add just a little bit of brown to him and I didn't use a whole lot of water because the more water you use the more you're going to pick up color underneath as well so if you want just a little wash of it he's just a little tiny bit and here I am trying to add eyes and nose and that bunny just look terrible so now I know better to do a little better job on that one but as a key card a little swatch like this it's going to work fine still because I will at least know how big it is because it's sometimes helpful to see them to scale and also to know whether they face left or right when you're looking at a cling stamp it's not like you can see it in the right direction because it's always reversed because that's where the rubber is so it's good to be able to have them stamped out like this this kitty set of course is adorable especially like kitties and they have one that's just the front of it so it can peek out of any container that you stamp and it can be behind flowers it can be behind another kitty can be behind a bunny can be behind anything and you can color them to match colors of your own kitties or the kitty that you're sending that's owned by the person you're sending it to that kind of thing lots of fun now there's one other thing I'm going to do here real quickly and I just bought a new marker so I'm gonna test it against these other markers this art and graphic twin I just bought the set of zigs and I wanted to try it out so this first one is distress and going to stamp that one this is the tombo it's the ones that I generally use the most with these art impressions stamps and this is the zig it kind of goes into all the work crevices so hard to paint on there with the marker since it has that brush and this one is the new zig twin the art and graphic twin and it goes on pretty heavy and it stamps pretty heavy so you'll see how that plays out when I add water to it really curious to see what a whole painting will look like with those so I will have some more images on my blog by the time this goes live I just wanted to get this voice over done so you're just gonna see this quick comparison so upper right was tombo this one is distress and the difference sometimes is in how much water you use or don't use but in general you can see the the tombo is holding up better it's not melting out and getting mushy as quickly the zig marker here is definitely getting mushy the now here is the new marker the art and graphic twins I am gonna have more videos coming up with them but this was my literally my very first little try at them they do have heavier pigmentation pigmentation that goes on the stamp and that is going to vote well for some techniques worse for others but I think it's gonna be interesting so stay tuned because I will have more coming up in the future on those and I will have links to all these of course in the do we do it over on the blog a quick reminder that you should probably pick up this set of tiny blocks if you're using these art impressions little tiny stamps very helpful and here's some images that are gonna be over on my blog as well one with all the kitties one with two bunnies one with just some flowers in the ornate containers and here I made one with a couple birds and the tree stump and a few of those boxes with one of the kitties so many possibilities for different layouts for scenes and this is two ways that I handled that cowboy boot in very different ways but so much fun to play with and I would invite you to do some swatching of your very own art impression stamps because it's really gonna be helpful as you start trying to make scenes if you get a whole lot of these you end up with lots of little great blogs to pick from so here's that playlist if you'd like to check that out and see more of the art impressions watercolor and be sure to check the links in the blog for all your shopping needs because you know that's the thing I'll talk to you guys later bye bye