Hello everyone. Sorry for the disembodied voice routine, but these sorts of problems, I think, require you to pay much more attention to what's written on the screen than my facial expressions. So what we're going to do here this time around is we're going to actually symbolize propositions. We've gone through truth relations, we've gone through terms and definitions, and now we're going to have to actually start assigning variables to sentences. This will result in kind of a calculus for these arguments. So the first thing, the first rule for these symbolizations are the variables, the letters that we're going to use to represent atomic propositions. I'm going to use these for atomic propositions. So the first rule is to use P, Q, R, and so on through Z for atomic propositions. Do this in order, right? Don't start with A, B, C, or D, and don't start with T, start with P. So this is the first rule, P, Q, R, and so on for these atomic propositions. One of the reasons why I'm being so personic about this is that you will be completing a homework on canvas, and there needs to be a uniform way for you to complete these return in these assignments. So it's one of the reasons why we have such strict rules. So what's this look like? Well, take a look at this sentence here, right? So we're trying to, again, follow this rule. Morality is justified by cultural belief. Only if our culture is morally impeccable. So just look at that first sentence. So the first thing you need to do is to identify the atomic propositions. And morality is justified by cultural belief. That's the first atomic proposition. That's the first atomic proposition. And the phrase here, only if is our logical connective. And only if, if you remember, gives us a conditional. And the only if, what follows the only if indicates the consequent what occurs before the only is the antecedent. And this gives us, this leads us to our second atomic proposition. Our culture is morally impeccable. Okay, so this is the first sentence. Morality is justified by cultural belief. Only if our culture is morally impeccable. So this gives us two atomic propositions and our logical connected. So this already tells us that we got a conditional. Okay, so let's just concentrate then upon this first rule and assigning a letter to the first atomic proposition. Well, following a rule one, the first atomic proposition, morality is justified by cultural belief. That will be assigned P. Okay. That's assigned P. So that's our first atomic proposition. What about our second? Again, following rule one, we got our second proposition here. Our culture is morally impeccable. That will be assigned Q. Right. So again, in order. So you so the first atomic proposition you get, that's assigned P. The second atomic proposition you get, that's assigned Q. That's our rule one. First proposition is assigned P. Second proposition assigned Q. Don't start with D. Don't start with T. Now you start with P and go on from there. And don't skip, right? Don't go P, T. So P, Q, R, S, T, U, V, W, so on. Okay. So we've got our truth assignment. We got our variables. Excuse me. We got our variables for our first two atomic propositions. Well, let's take a look in the next sentence. And the next sentence starts off with either. So that already tells us the disjunction. And more than that, we got either it is false set. So we got this should tell us right away, we've got a disjunction of negations. Let's take a look at the atomic proposition part. Our culture is morally impeccable. Well, this should look really familiar. After all, that's our assignment for Q. Now you might say, well, then I'll assign this R. No, this brings us to our second rule. Use the same letter for the same atomic proposition throughout the argument. That's the second rule. Use the same letter for the same atomic proposition throughout the argument. So our culture is morally impeccable. That gets assigned Q still, right, still. Okay, so I had here it's it's false that, right? Yeah, that tells us we got a disjunction. That's how we got a negation here. All right, even though this is a negation, right, the atomic proposition part still is assigned Q. This isn't a new time proposition is still the same atomic proposition. Also notice that we got, you know, either or happening here. Okay. That's so that that's another logical connective. And we got the second it is false that. All right. One of this brings us to, you know, it's always brings us to our third atomic proposition and the argument. And that's something needs to change in our culture. All right. So following rule one rule two, it's assigned R. And since it's a new proposition, that's why it gets R, right? Okay, so let's take a look at the next one. See if we have any more new atomic propositions. Well, the next one is something needs to change in our culture. Well, we just dealt with that. So it's so following rule two, it still has arm as its letter. And the last atomic problem we got. Yeah, however, however, it's just a connecting word. It's actually not even a logical connective. This is just more to indicate sort of mood sort of sort of thing. But sometimes that helps to use these sorts of connecting words in order to indicate the flow of the argument and that you're still providing premises, for instance. Okay, so the next thing we have is it is false that that's the logical connective. The word so there, I haven't highlighted it, but the word so that indicates the conclusion. If you remember from that, those sets of those sets of assignments are back there, that indicates the conclusion. And the atomic proposition part of it is morality is just by the cultural belief. Well, that was our first, a first atomic proposition. So it's still assigned P. So rule one and rule two, use P Q and R to for the atomic propositions, start at P, work in succession all the way up to Z, sign a letter for the atomic propositions. And if an atomic proposition gets a letter, use the same letter for all of it. Okay, so that's atomic propositions. Let's start taking a look at some of the complex propositions, complex propositions. So we will symbolize negations. All right, remember negation is a logical connective, although just, it's just assigned to the one letter. We'll use the minus sign for negations. And if on a standard QWERTY keyboard, that's Q, W, E, R, T, Y. If you never heard of this, right, this is the standard sort of keyboard where the letters are set up. And the you're looking at upper, you know, the second row, starting a Q, Q, W, E, R, T, Y. That's quite, that's why it's called a QWERTY keyboard. Little bit of nerd trivia there for you. On a standard QWERTY keyboard, we'll use the minus sign for negation. So that will go immediately before the proposition to indicate a negation. I want to be careful. Do not use shift minus, right? That produces a dash. That's a different symbol. The computer recognizes these two different symbols, right? Do not use a dash, right? Do not use a dash. So it's not shift and and then the minus button. Just the minus button. Okay. Just the minus button. All right. So we're going to assign a letter for each negation. Sign a letter for each negation. We're going to stick with this same argument, right? We'll stick with the same example that we're dealing with. So looking at this first negation here, it's in the second sentence. It is false that our culture is more than impeccable. And we got a second negation. It is false that something needs to change in our culture. Now, let's just go with the first one, right? It is false that our culture is more than impeccable. Well, we already signed a letter assignment to this, right? Where we saw that. So following rule one and rule two, and now our symbol for negation, this is given, you know, not Q, right? That minus Q, not the dash Q minus Q. And the second negation, you know, something needs to change in our culture, or it's false that something needs to change in our culture. Well, it had a assignment too for a letter, and that was R. So this is symbolized as minus R, minus R. And that's how we symbolize negations within the physiological formula. Let's take a look at conjunctions. To symbolize a conjunction, we're going to use the ampersand. That's what this thing is called, right? If you look at that little symbol above the seven, it's called an ampersand. So you produce that with a shift seven to produce that ampersand, or you might have just called it the and symbol. So that's what we use for conjunctions. Now, I have to change examples here to illustrate a conjunction. So there are fish in these waters, and this is good bait. So if we're going to sign, we're going to turn this into a logical formula. Well, first we have to identify the two atomic propositions. There are fish in these waters. That's the first one. And this is good bait. That's the second one. And we have the logical connected between and. So following rule one, there are fish in these waters, that gets P. Falling rule one and rule two, this is good bait. That gets Q. So if we're going to symbolize this conjunction, there are fish in these waters, and this is good bait. We use that with P, ampersand, Q. So I want to point out here, when we dealt with negations, there should be no space between the minus symbol and the proposition. No space for negations between the minus symbol and the propositions. For pretty much everything else, when we deal with conjunctions, there should be a space between the proposition and the ampersand and the falling proposition. And there should be one and only one space showing this. You have to be precise when you type this into the computer. Otherwise the computer is not going to count it wrong. It's not going to recognize that sort of simple error. So if we're doing a conjunction, we got the proposition, ampersand, and the second proposition, and that should be separated by space each. All right, let's take a look at disjunctions. Disjunctions, if you remember, give us subcontrariety. Or if we've got a disjunction of negations, that's contrariety. But to symbolize a disjunction, we're going to use just the lowercase v, not an uppercase, just the lowercase v. So just press the v button. So let's see what this looks like with our example that we dealt with. The either or indicates a disjunction. That tells us we've got a disjunction. And we also have to pay note to the negations, that those are in there too, the negations. So we had to account for those two in our symbolization. And these are our two atomic propositions. Now, so we've got to keep in mind, we already covered how to symbolize negations, so we're going to use this here in our symbolization, but we also got the disjunction. Now remember following, so our proposition here is either it's false that our culture is morally critical, or it's false that something needs to change in our culture. Well, remember following rule one and rule two, that first atomic proposition got q, that second atomic proposition got r. And we looked at how to symbolize the negation, so it would be minus q and minus r for the two negations. But then to symbolize the disjunction of those two, we have that little lowercase v in the middle. And again, there's a space between the first proposition and the logical connective and the single space between the logical connective and the second proposition when dealing with the disjunctions. The minus symbol, not similar to that, minus symbol needs to be right up next to the proposition. But the disjunction and conjunction, there's a space separating the logical connector from the two propositions, from the two disjuncts in this case. All right, let's take a look at conditionals. Conditionals are a little different. We're going to use the graded end symbol, so that's right over here. Or you might think it was a right arrow symbol, if you really want to think of it that way. And you use it by pressing that shift button and that button there for the right arrow on the quarter keyboard. And that's going to give us the antecedent will be on the left hand side of the symbol, and the consequent will be on the right hand side of the symbol. Okay, so we've got our example here, and it has it happens. We've got a logical connected that indicates a conditional. Remember that? And we have the two atomic propositions. And following rule one and rule two, if you remember before that first one got a P and the second one got a Q. So that's our conditional. And that sentence there is our conditional, it's justified by our culture, only if our culture is well impeccable. So following rule one and rule two, we've got P, we've got Q, and we've got that right hand symbol right in between, or is that the right arrow symbol, that graded end symbol right in between. And again, there's a space between the first proposition and the logical connective. There's a space between the logical connective and the second proposition. We want to make sure we get that right. So that's how we're going to symbolize a conditional. Now, keep in mind that conditionals can be written in a couple of different ways. So look at this. We've got, we've got to change around a little bit. Our culture is more impeccable if morality is justified by our cultural belief. All right. Now remember the difference between if on the one hand and only if on the other. If it's only if that indicates a consequent. That's what we saw last time. But in this case, we've merely got if, but that indicates an antecedent. Remember antecedents will not always be written first within the sentence. Okay. Now, since the order of the time of propositions has changed, their letter assignments has also changed. And remember, following rule one, the first time of proposition gets P. The second time of proposition gets Q. Right. Well, in this case, our culture is more than impeccable is now assigned P. Whereas in the example before, since that proposition occurred second, it was assigned Q. But this time it's assigned P. And the consequent now, morality, excuse me, the antecedent is morality is justified by our cultural belief. Since that occurs second, this time it's assigned Q. So instead of P greater than Q, right, instead of the P with that point Q, the order is reversed because of how they, you know, whether it's a P or Q, that's reversed now because of the order of their presentation within the argument. So conditionals are going to throw you as far as this is concerned. Right. Conditions are going to throw you whenever you got a disjunction, whenever you got a conjunction, you'll always be able to just put them in the order that they appear. That's not an issue. Conditions are going to be the weird ones. Which one is sufficient for the other? That matters with conditionals. Right. That matters. So you'll want to be careful with this when you be aware. So the first thing, right, when you see a conditional, find the antecedent, find the consequent. Whatever has an only if following after that, that's a consequent. Whatever has an if following it, that's the antecedent. Okay. So keep an eye out for that. Now most of these, now most, at least some of these arguments are not going to have atomic propositions as their components. And remember, I told you complex propositions can have complex propositions as their components. Now, when that happens, you need use parentheses to group together, you know, the smallest grouping, so to speak, or the smallest grouping of atomic propositions with logical connectives. So we'll use the parentheses to indicate the smallest grouping of atomic propositions connected by connectives. You know, two or more connected by connectives. So to use the parentheses, just so you know, we got, here they are. Use the shift button with the nine and the zero. Now the parentheses, the left hand parentheses should always be right up next to that proposition on the left. And that close parentheses should be right up next to the proposition on the right. So there shouldn't be a space between the parentheses and the propositions that it's enclosing. You might need to have a space outside the parentheses. That's, you know, that depends upon which connective you're using. But the parentheses should always be right up next to the propositions that it's enclosing. So we use these parentheses here for that. Okay. So here's a proposition. Morality is justified by cultural belief only if our culture is morally impeccable, and it is false as something needs to change. Okay. Now, immediately, you might be a little confused by this sentence, because it kind of looks like this, right? P, conditional, Q, ampersand, not R. Well, this is not a proper, this is not a proposition that expresses a logical, expresses a truth relation, right? We don't know if the truth relation is supposed to be indicated by the ampersand, or it's supposed to be indicated by the conditional. You know, we could have either one of these here. It could be a, this sentence could be a conditional, where the consequence is a conjunction, or the sentence could be a conjunction, where the first conjunct is a conditional, and the second conjunct is a negation. We've got two possibilities here. And even when you're reading, you might get confused as to which one it's supposed to be. You know, this is why grammar is, grammar punctuation is very important. So I want to show you two differences here. So the one on the left is where we have the conjunction, and the one on the right is where we have a conditional. Now, what's supposed to be the big difference between these two that indicates which one? Well, it's this little comma right here. That's the difference. That's what tells us whether we're dealing with a conjunction overall, or conditional overall. And there can be complex propositions within complex propositions. That's fine, right? I'm not complaining about that. This is a good thing. It, you know, it can be complicated after a while, but these are complex thought to express. But if you're going to express these properly, you must use proper punctuation. In this case, the comma makes all the difference. If the comma hadn't been there, this would be a conditional. This would be a conditional. But the comma is there. So we've got a conjunction. And this is how we properly express this complex sentence with complex, as a complex proposition with complex propositions as the conjuncts. So again, look, take, you know, take a close look at that, how the parentheses are used. That parentheses is right up next to the P for the open parentheses, and that closed parentheses is right up next to the Q. Don't have a space between between the parentheses and the conjunction and the proposition there. Okay. Now, this brings us to sequence. Now, sequence is when we take these formula representing the parentheses and the conclusion. And we use, we have just a single string of symbols to represent an entire argument. We're going to use this to express an entire argument. So with this, we got rule one, rule two, well, we're going to need further rules. Let rule three, list the conclusion last, always list the conclusion last in the sequence. And to indicate that you got a conclusion, we get two vertical bars and a space after the vertical bar, and then the conclusion. So for the vertical bars, again, on a standard quarter keyboard, you'll find them right here using the shift button, and that backwards leaning dash, I think it's called a back dash. Anyway, you find them here. That's the vertical bar that I'm talking about. That's the vertical bar I'm talking about. So let's write a sequence for this argument. Again, we got our example here. And that word so, that indicates our conclusion. And you remember we got morality is justified by cultural belief with the, is false that. So our conclusion is it is false that morality is justified by cultural belief. Now, if you remember, following rule one and rule two, when we saw that earlier, morality is justified by cultural, that was already given the truth, the letter p. So you still follow rule one for the assignment of letters and you assign them in order. And so we know that that gets minus not p as the conclusion. Okay, so that's the rule covering conclusions. We got a space. I'll explain, I'll say this again in a little bit, but say we got the last proposition for the premises, a space, two vertical bars, and then the conclusion. So the rule four lists the premises in order they appear in the argument and each is separated by comma. Okay, so we have the conclusion, we already brought that out. And we've got our first, we got our first premise here, morality is justified by cultural belief only if our culture is more than impeccable. Following rule one or rule two, that first atomic proposition got p, the second atomic proposition got q. We have them connected using our conditional sign that right pointing arrow, so to speak, or the greater than symbol, it's the greater than symbol. All right, so that's our first proposition. That's the first sentence, that's the first proposition, it gets a comma right after it, put that comma right up against the end of the first premise, but then a space after the comma. Second proposition, we've got that either or, so we know it's a disjunction, we've got the negations, so we know it's a disjunction on negations. Our culture is more than impeccable, that already got assigned q by rule one and rule two, so it's using the same proposition through there, and something needs to change in our culture, that was assigned r. So we had this not q minus q space, little v minus space minus r, and now we got the comma. So that's our second premise. This brings us to our third premise, however, something needs to change in our culture, that however, that's not a logical connective, it just helps us to understand what's going on within the sentence. So it's not actually symbolized by anything, something needs to change in our culture. Well, that was already assigned a letter by rule one and rule two, before it was a negated atomic proposition, now it's just the assertion of the proposition. All right, so there's no, it's just an atomic sentence. This premise here is just an atomic sentence. So it gets r, notice the last premise you don't get, there's not another comma, right, there's just a space between the last premise and the two vertical bars, then the space again, with the conclusion, with the conclusion. This is how your sequence should look, pay very close attention to how this is written, because the computer is going to be looking for exact entries for these answers. So don't do this, right, don't start squeezing in spaces, you know, don't forget the space between the comma and the premise, and don't forget the space between the conclusion, the premises, and the vertical bars. The vertical bars shouldn't have any spaces between them, but there should be a space on either side of the vertical bars. Especially don't do this, don't just type in a string of letters, the computer's not going to recognize what's going on, you have to separate these letters from each other, you have to separate the propositions from each other, and on the other hand, don't put in too many spaces, right? Don't just start putting out space between everything, no, take a look at that minus q, that's wrong, that negation symbol needs to be right up next to the proposition, the vertical bars, notice they have a space between them, don't do that, don't put a space between the vertical bars, okay? Just reiterate, this is what a proper entry looks like, and this is how you have a proper entry for this, okay? So let's take a look at a few practice exercises. So the first sort of exercise, you'll need to select the right formula given, you know, the question, right? So this question asks for a conjunction, which formula is a conjunction. Now this is pretty straightforward, this is not, you know, a mystery as to what's going on, you know, a conjunction is represented with an ampersand, and we see that with the third option, the bottom option is the greater than symbol that's for the conditional, the top is the lowercase v, that's a disjunction, the second for the top is the v, that's a disjunction, and the top is negation. So you just, you select the correct formula. Now, you know, the way to do this is you look for the connective, right? You look for the connective, and you remember, okay, conjunction is the ampersand, and you know, there you go, you see right there. Now, while that one's pretty straightforward, some of these can get a little complicated, especially when we have complex propositions within complex propositions. So you need to pay attention to the negations, right? And you need to pay attention to the parentheses. So looking at the bottom one, that bottom one there is not a negation, overall. There are negations in it, right? That's a complex proposition with negations in it, but overall it's not a negation. That bottom one is a conjunction of negations. Look at the second from the bottom. Overall, even though you have got the parentheses, right? And we've got negations, but overall that is a disjunction. That's a disjunction. Look at the main connective there in the middle, right? You can see that with this one, what really gives you the clue here is the parentheses for starters, right? So that parentheses gives you a complex proposition within the complex proposition. So that tells you that that should give you a clue as to what's the main operator overall. And so yeah, in this case, that's the disjunction. Go up on the second from the top. Overall, again, there's negations in there, but it's not a negation. And overall, it's a conditional. It's a conditional. So it's a conditional with negated and with a negated antecedent and negated consequent. The top one is actually the negation. It's the negation of a conditional, right? So it says it's not the case that if we think you it's a negation of a conditional, but the components of the conditional are not themselves negations, right? So the top one is a negation of a conditional. The second from the top is a conditional with negations. There's a difference there. So again, there's this top one here, that's actually the negation. Okay, now this sort of questions, a different sort of questions that are just merely identifying the kind of formula, right? Now you're given a sentence in English and you're supposed to find the formula that represents it. So you have to look for the connective here. Look for the right connective. So you have to look at the sentence itself. The animal is a llama, so the animal is a mammal. Well that word so there, that's the connective. The animal is a llama, that's a atomic proposition. The animal is a mammal, that's another atomic proposition. All right, so what sort of connective is so? Is it a disjunction? No, it's not, right? Oh, it's not. The connectives for disjunctions were or or unless, either or or unless. What is word so supposed to indicate? Well, it gives us a kind of inference, right? From the first one to the second, right? So is that a conditional? Yes, it is, right? So that's what the other three are, right? We got the other three, we got three conditionals here, okay. Well, we've got, you know, if P, we've got a conditional with P, greater than Q, right? There's a P conditional Q. We've got not P conditional, not Q, that's the third option, and then P conditional R. Which one is it? Well, are there, so we have to look for negations. Are there negations here? Well, you don't see any negations, right? The animal is a llama, the animal is a mammal. These are both assertions. These are both affirmative, okay. So we know it's not that third one from the bottom. Well, then we have P conditional Q and then P conditional R. Well, these are both conditionals, and they both kind of look right, you know, so what's supposed to be there for between them? Pay attention to rule one and rule two, right? For rule one, you assign P to the first term proposition Q to the second. Well, then that leaves out that bottom proposition, right? That, for that bottom one, R is assigned to the second proposition, but that breaks rule one. That breaks rule one. So you have to pay attention to when, pay attention to the assignments for the letters to ensure that you're following rule one and rule two. So what's that second one? That's the right one, P conditional Q, okay. Here's another one, right? What's the correct formula? I exist if I think. Hmm, what's the connective? Well, the connective is if. Now, this should immediately send up an alert, right? We've got a conditional here, but we know there's an issue between if and only if, right? Well, if it's only if, then that only if indicates the consequence. But here we just have if, and if we just have if that indicates an antecedent, okay. So take a look at our options here, not P, look at the top one, if not P, then not Q. Well, we're going to roll that one out because there's no negations within this sentence. We've got if P then Q, well, that's a conditional, there's no negations that already looks right. We've got if P then R, so again another conditional, but no negations that also looks right, and the last one if Q then P. Oh boy, yeah, what are we supposed to do here? Now we've got three that look right. We'll take a look at the second from the bottom. We already talked about this, right? Following rule one, that R is out of place, right? And there shouldn't be an R, should be a Q. So then we have if P then Q, and then if Q then P, well, it looks like then it should be if P then Q. But remember, if indicates the antecedent, right? I think it's the antecedent and following rule one, that will be assigned Q, right? I think in the proposition that word if there indicates the antecedent, I think it's the antecedent. So that's given Q and then I exist is P. And so that's the bottom one, that Q conditional P. That's the right formula for this sentence. Be careful when you're translating. Watch the placement of letters in the conditionals. Watch if and only if, right? You got to pay attention to which one's given to which, if indicates the antecedent, only if indicates the consequence. So again, it looks like it might be between these two, or even that third from the bottom one, but it's only this one. It's a Q conditional P. That's the correct formula. All right, looking at this one, notice we've got Q conditional P, right? So for the others, we had translating from a sentence to the formula. Now we have a formula to a sentence, okay? Now we have a formula to a sentence. So what do you think we should do? Well, take a look at the first things first, take a look at the connective. The connective is a conditional. Well, the first option is or, well, that's a disjunction. So that's not the one. The second option is, you know, if then those are the those are the connectives there. Okay, well, that's a candidate. The third option, the figure sides are parallel. If the figure is a square, that's also a conditional. And then the last one, the figure squared is a parallel and the figure is a square. Well, that's a conjunction. So that's the choice between the second and the third. All right. Well, how do we distinguish between them? Well, pay attention to the order of the letters in the sentence. That should tell you something. The, remember the order, which is supposed to do is go from the sentence to the letters, you're supposed to sign the first atomic proposition, the P, the second atomic proposition, Q. So already, since we have Q right there, what we're told is, what we know from our rules is, the antecedent is the second proposition, second atomic proposition. Well, that happens in the third one. We've got that if the square, the figure is the square, that's the antecedent, it's indicated by if, and it's the second atomic proposition. So that's why it gets if Q then P. All right. So now we have a complex proposition of complex propositions. Overall, what sort of formula is this? Is this a disjunction? No, there's no disjunction conditional. No, just no conditional. We've got negations here, but is this overall a negation? No, no, this is overall, this is not a negation. This is a conjunction overall, it's a conjunction of negations. All right. So let's take a look at the sentences. The first one says either or, right, well, so that's a disjunction, we figure that out, so that's not it. The second proposition, the connective is if then, so that's a conditional, well, that's not what we're looking for. The third one is either or. Okay, so that's a disjunction. Well, that's not what we're looking for. We'll find the last one candidate left does not win the election and candidate right does not win the election. That's the conditional of negations. Be careful when you look through, you want to make sure you pay attention to negations. You want to make sure you pay attention to the to the connectors for disjunction, conjunction and conditional. Make sure you're matching up the right ones. So for the next sort of problem, you're given an argument and you're supposed to assign the atomic propositions. Now we've been rather helpful here and I've indicated, right? So we have that. So just looking at all truth is relative, but that's our first atomic proposition. I've been helpful here and already telling you where the atomic propositions are. So you just have to start assigning the letters according to rules one and rule two. So you'll hit that select button there on the screen and it'll give you a little pulldown menu and then you select the proper assignments following rule one and rule two. So the first one all truth is relative. That's the first proposition. It gets P. We had to assign that P. So you select which letter to use and then for keeping in mind for rule two, right? So I have this atomic proposition. If there's some absolute truth while following rule one, it gets Q. But you have to look out for the rest of the argument. Notice that proposition also pops, atomic proposition also pops up down here near the bottom. So it needs to get Q two. So you can't just go through the list of first one P, second one Q, third one R, fourth one S. In fact, if you notice there's, you know, this P through U for the pulldown, you may not use all of these. It was one or two where you're going to use all of them. But for some of them, you're not going to use all of the letters. So you're going to need to pay attention to rule one and rule two in order to assign the proper letters. So for the, so this is a similar sort of problem, except in this case, instead of a pulldown menu, you type in the letters, right? You type in the letters. So you look for the atomic propositions. And in this case, right, I've got the blanks here. So you know that that's the atomic proposition. I've helped you out with this. You don't, you know, you don't need to discern the difference between the time of proposition and the complex one. But you need to pay attention to which atomic proposition you're dealing with, because some of these might pop up, you know, more than once. So for instance, that first atomic proposition, either person is either a person, excuse me, a person is pursuing a good life. That's the atomic proposition. Well, that pops up again, several times, right? If you notice in that second sentence, there it is. A person is pursuing a good life. Well, that needs to get, so the first time you see it, it gets a P. The second time you see that a person is pursuing a good life, like it's a P there too, following rule one and rule two. So you need to pay attention to where those, if it gets a letter, one point on the argument needs to get the same letter throughout the rest. And in this case, as I said, you are typing in the letter. You're typing in the letter. So you're going to type it directly into the blank. Okay. Make sure it's capitalized. Make sure it's just the letter. Don't type anything else besides that. So this question, sort of problem, you have to put it, you have to type in the P, the Q, the R, and so on. For the next kind of problem, you have to type in the whole formula. Some of these will just have one formula. Some of these will have as many as three. This one actually is three. So it's not just notice a change in the instructions, right? You know, symbolize the following proposition, not just putting in the letters, you're symbolizing the whole formula. So the whole sentence. So that first sentence, if one talks about nothing, then either nothing is a subject or nothing is a predicate. Now it's kind of fun about this case. Right away. You got to watch out for parentheses when necessary. You got to watch out for those parentheses. So in this case, we got that either or happening right after, right after the then with the consequent for the conditional.  No, it doesn't, right? Because that either is contained, just immediately within the consequent. The either or they always have to go together like that. So this is a conditional, right? This is a conditional with a disjunction in the consequent, right? So it's going to look like that. You got the conditional with the with the disjunction in the consequent. Okay. So make sure you pay attention to the parentheses when necessary. That's that'll pop up. And not always, right? Look at that second sentence. If nothing is a subject, then one can describe nothing. That's just a straight up conditional. There's no complex propositions within the conditional. Okay. The last kind of problem, you're going to need to put in the entire sequent. And so this is going to require pretty much all the skills that we've been developing so far, right? We've had to, you know, we have to identify the premise and the conclusion. You have to assign atomic letters to the you have to identify the atomic propositions for the complex. You have to assign letters to the atomic propositions using rule one and rule two. And this one you have to deal with real rules three and rule four, right? Rule three and rule four. Remember, rule three, you got to put that conclusion first. And then you put in the premises in order. Now, this one's kind of straightforward, right? Because we see that as far as identifying the conclusion, we got that therefore, if we're sometimes mistakenly perceptually, that indicates the conclusion. And so, you know, the rest of these sentences in this argument are premises. And you'll type them in that box that you'll see right there. Here's another example.  Rule three says, list the conclusion last. All right. In the sequence, list the conclusion last in the sequence. Well, if you're reading this, say the first sentence, either a person is pursuing a life of happiness or a person is pursuing a life of misery. Four, either a person, so that four indicates a set of premises that follows. So that first sentence there, that's the conclusion. And that's the conclusion. Following rule three, you'll list the conclusion first, a space before, you have a space, then the two vertical lines, another, you have two vertical lines, then another space, then the conclusion, the conclusion itself is a disjunction. Following rule one and rule two, it's the first atomic proposition gets that P, the second atomic proposition gets that Q. So it's P or Q. And then you'll follow the rest of the rules, you provide the premises in order separated by comma. Okay, let's take a look at this next one. It's false that one could talk about nothing. If one could talk about nothing, then either nothing is a subject or nothing is a predicate. If nothing is a subject, the one could describe nothing. And nothing is a predicate, the one could describe, can be described as nothing. It's impossible to describe nothing. And it's impossible to describe something as nothing. This is difficult. We have no indicator words. We have no indicator words telling us which one is a conclusion. Well, try to look at the under, try to comprehend the meanings of the propositions here. Right? How is, how is the reasoning progressing? Now the first sentence is negation. Right? So following rule one, it gets assigned P and it's the negation, not P. The second sentence has that same atomic proposition, except in this case, it's not negation. Right? The first atomic proposition, sorry, the first complex proposition, the first sentence, it's false that one could talk about nothing. One could talk about nothing is the atomic proposition. That's P. So that's not P is that total complex proposition there. Look at the sentences. If one could talk, you know, if one can talk about nothing, it's like we just completely ignore the negation to begin with. And it goes into this line of reasoning where at the end, this is, well, by the way, if we assume that we could talk about nothing, then we reach these impossible conclusions. Well, if we reach a possible conclusion, that first assumption has to be false. This is a difficult one, but that first sentence again. In this case, it's also the conclusion. This isn't always going to happen, but sometimes it will happen. Okay, so when we are typing out the premises for this argument, so we got our conclusion, we're typing out the premise, it kind of gets cut off in the box, but that's all right. Don't worry about it. Just make sure you type it in there correctly. It should be fine. But you notice we've got several complex, we've got complex propositions within complex propositions. We've got complex, if one could talk about nothing, then either, that tells us that the consequence is a disjunction. The second one, that the subject is another one, that's a straight up conditional. So when you're translating, you've got to spot the connectives really fast. That helps identify the atomic propositions. That helps you rule one, identifying the atomic propositions, making sure you have the same one assigned to follow rule two, and help you identify the premises in the conclusion. The connectives are really key for figuring that part out. This is just yet another example, right? So this is what a completed, oh, I'm sorry. This is not a completed example. Sorry, I want to tell you, watch out for a couple of things. Don't leave your sequence with a comma separating the last premise from the double vertical bars. Your last premise should not have any commas. Don't leave an incomplete sequence. If you do either one of these things, you're not going to get any credit, the computer is programmed to recognize the sequence. It can't recognize meaning, it can only recognize a string of letters and symbols, right? So you have to type it in precisely following all four rules that we've been given. If you miss something in there, it's going to count the whole thing wrong. This is kind of another tricky one. That what's within quotation marks, that's itself not an atomic proposition. That believe it or not, that whole first sentence is an atomic proposition. Or excuse me, it's a complex, sorry, it's a complex, right, with negation, right? The atomic proposition would be there is empirical content for the claim all knowledge is empirical. That would be the atomic proposition, right? That says there is this thing. That's the atomic, since it got the no in there, that makes it an negation. So you have to be careful to spot the difference between a sentence that's mentioned within a sentence and the atomic proposition itself, right? Sometimes a sentence with mention within a sentence can be an atomic proposition. You have to pay attention to the meaning of the sentence. Make sure that when you type in your sequence, you have the proper spaces. This is incorrect. It will not work out well. If you do this, make sure you put you have the all the premises and make sure you have the premises and the conclusion. Otherwise, it won't count. All right, so that's kind of a rundown of all the kinds of problems we have for this chapter. Good luck with it. If you need to come by my office and talk about this, I'm more than welcome to see you.


We've been describing motion using our normal everyday language throughout our whole lives. In physics we sometimes have to be a little bit more careful, so let's just take a few moments to recap some of the concepts we've introduced and look carefully at their definitions. So we normally describe motion in the real world in three dimensions, and that's a little bit tricky, so for this discussion we'll just talk about travelling along in a particular straight line. And as Vanessa's already discussed, what we need to do in order to describe that we need to be able to say where things are, so we need some kind of coordinates, so we have a zero in position, and then if we're at a particular position up here, we say that we are a distance x from that origin, and that position might change over time if we're moving around. So one of the things we have to be careful about to distinguish in physics is the difference between displacement and distance. Supposing I started at the origin and I travelled all the way over here, and then turned around and came all the way back to here, and so I ended up at that point there. Now if I'm there, the question you might ask is how far did I travel? And there are two perfectly reasonable answers to that. One answer says, well, I travelled that amount of distance, and then I travelled this bit back, and so I have to add that together, so I add those together, and that's how far I travelled. Another perfectly reasonable answer is, well, I only got that far. So that's how far I travelled. And those two answers are given different names in physics. The one where we have the long trip is called the distance you travelled, and this difference between where you started and where you ended is called the displacement. When we start worrying about directions of things again, we'll notice that distance doesn't have a direction. Distance is a scalar quantity, whereas displacement does care about direction. If I'm there, that is a different displacement to there, and so displacement has direction, and when we're just on a line, it can only be positive or negative, but that means it's a vector quantity. We can talk more about how to deal with vectors that aren't all in one line later. Now if we want to talk about something moving around in time, a good way to describe that is with a graph. And so if we have a graph of position as a function of time, then if they're not moving at all, they'll stay at the same position. And if they are moving, this will have a slope, and if they change the slope, that means they're going to change their velocity. And it turns out that in physics we make a distinction between speed and velocity, and it's exactly the same distinction we're making up here. So the speed is just the total distance travelled divided by the time taken. And so that's a scalar property, just like distance was a scalar property.  But your displacement was quite small, because you ended up almost back where you started from, and so that means your velocity is low. So velocity is a vector, because it's got a direction. So if you travel backwards, then you have a negative velocity. So the velocity here would be zero, the velocity here would be positive, because x is getting bigger over time, and the velocity here would be negative, because x is getting smaller over time. We've already spoken about the difference between instantaneous and average properties. And so if we look at a very small piece of time, of time delta t, then a particle moves a distance delta x, and our instantaneous velocity is going to be just that delta x over delta t. So while you might use the formula that the velocity is a change in position over a change in time, it comes up in a lot of different contexts. You have to make sure whether you're talking about things like average velocity or the instantaneous velocity. And of course, most commonly, the velocity is changing over time. Or there might be more than one thing, so there's more than one velocity. So whenever you're dealing with a real problem, make sure that you draw a diagram and make sure that you write the particular symbols you're talking about, and you're very clear, and use words to describe what you're talking about when you talk about these symbols. And the situation where the velocity is changing is where there's an acceleration. And just as the velocity is the rate of change of displacement, the acceleration is the rate of change of velocity. Now, acceleration doesn't have a scalar version because by the time you're talking acceleration, you're normally talking to a physicist, in which case you're normally talking about the vector quantity first time. However, we do use acceleration in day-to-day life. For example, you might say, I'm going to jump in my car and I'm going to accelerate. So I press the accelerator, and that makes me go faster. And people are happy that that means acceleration. But what happens when I press the brake? That slows me down. Well, to a physicist, that's still acceleration.  And so you're accelerating backwards. So acceleration is a vector quantity. Another example of acceleration that typically is not understood as acceleration is where you're changing direction. Supposing you're in a car and you go around a corner, even if your speed says exactly the same, people might say that therefore you don't accelerate because you're not going faster or slower. But because your velocity is changing, because remember velocity has direction in it as well, that means you must be accelerating. So something has to happen in order for you to change that direction. And you'll find that very clearly if you try and turn a corner in a car and the road is very icy. If you don't have friction with the road, you don't get to change your velocity. And once again, of course, you can talk about an instantaneous acceleration or an average acceleration, exactly the same sense as you do for velocity. An instantaneous acceleration is the acceleration defined over a short period of time. And an average acceleration is the acceleration defined over some large period of time.


Welcome to Rehash. On the internet we're all news, he's old news. We bring you the best and worst of what's happening today. Thank you so much to Live Action Liam for his introduction, if you'd like to provide one of your own, link is in the description where you can provide one. So I have a newsy type thing, you have a newsy type whatever. So I wanted to talk to you guys about the Top 10 Pre-Order List for E3 and along with that, Crazy Battlefield 4 Physics. And today I wanted to talk to you about Team Mobile and how the CEO is painting himself as some sort of Batman. All right, you know what, I'm going to let ladies go first. Thank you so much. So E3 just got done, a few days ago it just got done. It seemed like everybody's milking that, really. I was excited, I actually didn't get a chance to even watch it. I've been seeing glimpses of trailers. I know, I feel like I'm coming into everything later, so we apologize about that. We've been doing a lot of E3 things. I've been watching it every single year, the live event. And this year I just didn't have time. The time zones were so drastic. But regardless, I'm still catching up on everything and I'm assuming you are as well. But I want to talk to you about the Top 10 Pre-Order List that you guys have pre-ordered games for. So the very first one is Rare Replay by Microsoft. This is a game of a studio that has been around for over 30 years and they're redeveloping or remastering a lot of their older games that they've made. Interesting fact, some of the older guys from Rare, not only old as an age, they've been there forever. They left and they've started their own company and they're creating a new spiritual successor to Benjuk Zooey. And it's called Yooka-Laylee, they actually just finished a funding campaigning thing. You know, I see it early, they were asking for like 175,000 what pounds of euros and they had like 2 million. So I think it's been pretty successful. I think that that game had better come with like everything. And then the rest of the games go as follows. We have Gears of War Ultimate Edition, we have Doom, which as a kid growing up, I've got a lot of it, Dishonored 2, Final Fantasy, I'm not sure what that number is because there's so many of them, Gears of War 4, South Park, The Fractured Butthole. Butthole. Butthole. Right, butthole. Okay. And then we have The Fractured Butthole and we have Horizon Zero Down, Dishonored Definite Edition and then Xbox One Elite's Wireless Controller. I'm actually surprised that South Park isn't higher on that list because of the way that they were kind of playing two gamers by that stinger that we were talking about at the end of their trailer. Yeah, I can't believe that they didn't bump them a little bit higher on the list because everything that South Park does, they do with this like self-conscious, like, you know, they know that it not anger people, but that, you know, some people are let down by freeers. Oh, I mean, they tell the truth, yeah, that's what it is. Okay, so, and I wanted to talk to you about this clip that includes the T-Mobile CEO as some sort of comic style Batman where he talks about what he calls a duopoly, AT&T and Verizon looking to control all mobile bandwidth and something that you can do to stop that if you'd like, and I don't know, it's just interesting that he paints himself as the hero, like, though it may be the case, maybe he's, you know, doing this for benevolent reasons and whatever, I don't know, it kind of seems like an ego-driven thing, just a little bit, but it's definitely an interesting watch, link is in the description if you'd like to watch the whole thing, and then not to the comments. Comments A, B, T, D, I don't know what's after that. First comment I'd like to go over is by one Mr. Zero Mizukin, I'm assuming, I don't know. I think he did pretty good, because if I attempted it, it would be a lot worse. So he says, hey guys, it would be awesome if you had an option in heartbeat which would tell if a video or a song is copyrighted, and I mean, not your video, or our video, just one of the analytics options, so on and so forth, comment is on the screen now if you'd like to take a look. So the problem with this is that we can't have, yeah, copyright is such a massive thing, like massively, massively massive, like it doesn't take a whole lot to get a copyright on something, and to have an all-inclusive list, or you know, maybe even a function where something listens or watches and says, yep, that's copyright, it's impossible, keep this in mind, okay, copyright is a very touchy subject because a lot of people don't understand it, and I don't want to say much that's going to lead people to misunderstand, but every time you upload a video that you 110% make, you own the copyright on that. That is how copyright works, and there's a piece in copyright law that allows people to use small sections for certain purposes called fair use of copyrighted material. It's not a very clear-cut thing. The best thing that you can do for your channel is to study copyright and make sure that you are on the right side of the law. No, I'm not trying to be gimmicky here, but like literally if you do go to the, like I think it's like Google website, but a YouTube homepage, like I, before I started making videos, I read every single article they made, every single article. And we'll definitely also make sure to link down below to the US government's pages and articles on fair use so you can read through this. It does take a long time to kind of get a feel for what is and is not fair use. But the thing about it is if you're doing YouTube to like not only have fun but to make it evolve into a career, it's something that you literally need to know. Because what if you get three years down the road, you don't understand copyright now, but then you do, and then you're making content now that's copyrighted. So what if you get a million subscribers? The content you're making now is all copyrighted and your channel's gone. It's really worth going to. Okay, and I've got another one here. Let's see here from Kaiser Herzen, who we've actually featured just the other day. And he says, have you heard of micro-general drones? They are the size of a hummingbird. I actually have heard of these things. Yeah, I've seen a video of them. They look just like birds. When I was white water rafting with our boss the other day and got this horrible sunburn and all that stuff, we actually saw one. And not only are they the size of hummingbirds, they sound like insects when they fly.  He says, you should have coffee cups on the table and dress up in monkey suits. Hashtag sophisticated rehash. I don't know if we can do the monkey suits, but we can definitely do the coffee cups. We can do suits and ties. Then we'd be styling like that one guy from the Backstreet Boys.  You can buy a whole bunch of coffee cups, like take them on the wall and just go. I'm pretty sure that's like using coffee cups improperly. I was pretty sure you were supposed to put liquid in them and set them up. And strengthen, yeah. I understand, I agree, but we got to make it happen. And just because Zack said that he was going to wrap things up, he didn't consult me on this. I've got one more just to spy on. Oh, okay. Yeah, I see what it is. Yeah, so Aim Games or The Aim Games says, Zack just did a PewDiePie moment at four minutes for all seconds. I'm not entirely sure what that means because I can only watch so much PewDiePie. Why did they tend to try to aim to eat it? I just had a seizure at that time. Is that what happened? Yeah, I was like, can you do that again? Probably not. I can try. All right, can we slow that down a little bit? Thank you so much for joining us for yet another episode. We are trying to keep these a little bit shorter for you, the Freedom Family, because we know you want to get through your day. Let us know in the comment section down below. Do you like more news stories, less news stories? What do you enjoy most and least about the show? And what would you add that's actually something we want to do? We want to add a specific question, a comment question of the day, so that we'll talk about the next day or in the future. And that's our comment question of the day. What would you add or remove from Rehatch? Anyways, until next time, don't forget to like, subscribe, do all those things that make us love our jobs, and be awesome to yourself and amazing to each other. See you guys later. Bye Freedom Family.


Welcome to All Hands Update, I'm Petty Officer Ian Cotter. On May 28th, Secretary of Defense Chuck Hagel ordered a 90-day comprehensive review of the Military Health System, or MHS. The Navy's Surgeon General Vice Admiral Matthew Nathan worked with internal and external review experts to conduct the review. We want to be a health care system that's looked at as a marquee health care system, not only in combat casualty care, which clearly we are second to none in the way we can care for those in the wounds of war. But in our garrison and peace care health settings, our military treatment facilities, how can we raise the bar to be exceptional in every category? The review of MHS examined access, patient safety and the quality of care. Nathan said there will be more to come as the Navy aggressively implements changes to address the review's recommendations.


So here's a little bit of an overview of forces in equilibrium and non-equilibrium. Now as a reminder, when we're dealing with forces, we really care about the net force. And that means you must consider all the forces that are acting on an object. Direction matters. And we break it down into the x-direction and the y-direction. So these are our Newton's second law equations where we're taking a look at the net force in the x-direction and the net force in the y-direction. And again, this is the symbol for a summation, so it's the sum of all the forces. And when I take into account all the forces in the x-direction, it's related to the mass times the acceleration in the x-direction. And when I add up all the forces in the y-direction, it's related to the mass and the acceleration in the y-direction. So then we have equilibrium. Well, equilibrium simply means that all the forces are balanced. And that means my net force is zero. And that's for x and y. And technically z, but we're not doing very many three dimensional force problems yet this semester. So the sum of the forces in x are zero, and that gives me an acceleration in the x-direction, which is zero. And a sum of the forces in the y, which is zero, which means my acceleration in y is zero. So not only are my forces zero, but my acceleration is also zero. Now when it comes to this equilibrium then, there are two types. The first is called static equilibrium. And this is when the object's not moving. And if it's not moving, the velocity is zero. And if I have a zero velocity that's not changing, my acceleration is zero. So this object is in balance and not moving. The other type is dynamic equilibrium. And in this case, I am moving, but my velocity is a constant. Because remember, if you're moving with a constant velocity, your acceleration, which relates to the change in the velocity, is also zero. Now thinking about this, this is kind of like Newton's first law, which I'm not going to write it all out here, but remember, an object at rest stays at rest or an object in motion continues in that motion unless acted upon by an outside force. So in this case, I have no outside force. I have no acceleration. The objects continue the way they were. Now the other side of this is the non-equilibrium side. And here, the forces don't balance. And that means my net force is not equal to zero. And so that means I have to have an acceleration. This acceleration could be an x, it could be a y, or both. I could have acceleration components in x and y. Regardless, that means my velocity must change because there is an acceleration. So again, this is just an overview of what we mean by equilibrium and non-equilibrium when it comes to forces in general physics.


Good day, fellow investors.  Stocks go up and down all the time and I get so many comments on stock price this, stock price is down, what should we do? Is it overvalued? Is it undervalued? And that's unfortunately over the long term a losers game. On the other hand, you have investing where you buy businesses, own businesses and let wonderful businesses do the compounding. And that's what makes the difference in your lifetime. If we take a look at the Forbes richest people in the world list, you have Jeff Bezos, Bill Gates, Warren Buffett, Carlos Slim and Zuckerberg, Bloomberg, Larry Page, etc. etc. And how much trading did they do? How much undervalued, overvalued did they do? What did they do? They owned one business over their lifetime, they still own the business and they just let the business compound into infinity and become the richest person in the world. You don't have to be the richest person in the world but if you allow for compounding over the long term you will be very very well off. There is constantly comments about overpriced, underpriced and that's always relative. When you look at overvalued, undervalued, you always depend on the market. You have to move fast, you have to trade, work a lot but if you shift your focus from the stock price and that's difficult to the business. This is a business I like to own at this price. It gives me this and this return over the long term. That's what I like to own and then you simply compare it to other businesses given the return, given the growth, given the potential, the modes, the quality and you sell one business when you have something much much better. If this one gets overpriced from a business perspective, not from a market perspective and that's long term investing. It's a hard message to send, it's a hard message to explain but it makes the crucial difference when it comes to investing. So before buying a business next time, just stop for a second, get away from the stock market, from the stock prices, from the news, from the media and focus on the business, focus on what you're buying and think, okay if the stock market closes for the next 10, 20, 40 years and I cannot sell it, I have to own it forever. Would I be a happy owner of what I buy? The number of buys sells gets down, what you do is just buy here and there and if I find one, two businesses per year that fit that category, then I'm the happiest person in the world. And that's also what I do on my stock market research platform. The more and more we focus on great businesses and one great business that I found a year and a half ago was Catech Solar. Solar industry tailwind, great business model, cheap financing from international agencies, high return on capital and a lot of growth and I bought the stock a year and a half ago starting then increase the position and it's just a gift that keeps on giving and if it keeps on giving as it's likely to keep on, I'll simply hold it for ever and think oh, what a big chunk of luck did I have or a lot of research to find such a gem in the early days and that's something you have to understand. Yes, the stock price goes up and down but that's not investing, that's speculating. Investing, finding the great businesses and holding to it to infinity, allowing for that business to compound. And just a final long-term investment. If you find a great business, if the stock price goes down, you're a happy person because you can reinvest even that 2.2% dividend if you can reinvest it makes a huge difference over the long term. If you add your 100-500 monthly savings into that stock that the business that went down because I don't know why went down, then you compound, you multiply your investment returns over the long term. I hope this was great motivation for you to have a long-term mindset and if you like that long-term mindset please subscribe to this channel, click that notification bell and I'll see you in the next video.


Okay, so let's try this one. It's a percent yield question. It says a sample of lime calcium oxide weighing 69.0 grams was prepared by heating 131 grams of limestone, which is calcium carbonate What was the percent yield of this reaction? So I have taken the liberty to write down the reaction So calcium carbonate solid is heated up To form calcium oxide and carbon dioxide goes away. Okay, so we're left with 69.0 grams of calcium oxide So once let's define the percent yield, but since calcium oxide and calcium carbonate Way different amounts. There are molar masses different. We're going to have to calculate the number of moles and then compare that okay, so Calcium It is 40.01 if I remember correctly Plus oxygen which is 16, so we've got 56 0.01 grams of calcium oxide There's one mole of calcium oxide so Okay, so I get 1.23 moles Calcium oxide, so that's how much we produced. This is how much was produced in the reaction How much could we have so what was the theoretical yield? Okay, so this is the produced or actual So what's the theoretical yield? Well, we've got to go from the starting material to calcium oxide. Okay, so for one mole calcium carbonate Well, let's calculate So what do we say? 40.01 plus 12.01 plus 3 times 16 100.02 Calcium carbon like that right so that would give us the mass of calcium carbonate But we want to know what the mass of calcium oxide would have been if it all reacted so that theoretical yield So where do we get that molar ratio? We look over at the reaction equation So for every one mole of calcium carbonate goes to one mole of calcium oxide so 31 divided by 1.02 And I get 1.31 moles of calcium oxide. So this is what we call So the percent yield Remember it's the part divided by the total so in this case it's going to be the actual divided by The theoretical And this would be the number of moles Thanks, and now we're comparing the same thing moles of calcium oxide to moles of calcium oxide So we got 1.23 moles of calcium oxide divided by 1.31 moles of calcium oxide Moles of calcium oxide canceled and so 1.23 divided by 1.31 times 100% If we go to three significant figures we get 93.9%, I think if we look on the paper that answers that. Any questions about that one? No. Hopefully it makes sense. It really does. I'll get it.


I always wanted to see a Kala Masha Kau, you know, a hard stone. Those are petitions from the South Sea guys for Issa, and Nameless was really pushing it. We've aligned our street naming process in terms of how the community can ask. So you don't suddenly wake up tomorrow in Tsisakaja Road everywhere. You know me and the road named after me. But there are people who are not just the creative sector in the life of Nairobi. You know, like John Kaku, the mayor, Magic Mike. The guys who have done things contributed to this city that need to be recognized. And so for this space, we'll democratize it. And ask you guys, is there someone you recommend who we need to honor? There's a National Heroes and Honors Council that does it for the national level. But for Nairobi, we'll bring it down to us. Who are our heroes? We'll bring it down to us. Some people may not know what to do for years. And everyone has gone through our hands. She needs to break up next. It's not just the differences at Holy Road. It's the reloading away, Kenyatta. No, our local heroes. And so from the creative economy, you see the problem with the creative economy, which is just how we are creatives, at Medu Kupangwa. And so because of that, we see a kind of victory outside of something that we want to march on. You start yours according to Nini. Nini starts his. I wish one day we'd get into one creative economy thing for content creators. Because if you're not organized, you don't be recognized. You have no space on the table. And I keep saying, if you're not on the table, you're on the menu. So if you want to be on the menu, but I would want us, if you'd allow us, to structure something, would you guys accept to fit into it? In Takubali. So that he goes, he goes, he closed the door, he will begin, he closed. It should be collaborative. But the problem with democracy is that you hardly always act clean. So also leave a chance for leadership. 60% leadership, 40% if you don't agree, we'll tell you how. And if someone wants to engage, plug into it. We do that with Matiris. Matiris was the worst guys. Mouina, Apahapa, Aroji, Apahapa, these are the things that I don't listen. These are organizing you, on your corridors, on your routes. If you want to engage with us, use this platform. It's working perfectly. So we'll be able to do that. My brother and daughter decorate our cities, this is something we're doing. And actually I'd like you guys to plug into it. Many places you're seeing are not Instagramable. And they don't have iconic signs, like an Nairobi sign here. The thing we've had for a long time is KCC.  And the current creatives are finding spaces around poster, the old buildings. And so I was able to get 250 million sheniks to downtown CBD to make the pathways wider to create working spaces. And so I asked Justin to connect you guys with the technical team. So ITVP and Internet Europe. And so how do we get you? Who do you call? That's one of the questions. So we didn't pull it out. So you can come and say, if this street was designed this way, we'd get better photos. And the sun rises from this side and you guys know all those things that I keep learning every day. Facing this place, we need something this high because of people's general height to see. So we'll get a representative from you people who understands geography and film. How many of you guys are in the photography space? We don't know. We don't know. We just pulled it out. So we can connect multiple and we can make it longer. Because we're using this money now in a short while. So please plug into it now. So you can say now the fully looks like this and it's helping us do this. Another part of town would well go. I've said let's make it one way. Make it one way. Create bigger space from pride to nafuma barabara. Guys set up the umbrellas. Restaurants have your fresco lunches and what not. And more such spaces. It is arabo to ability that you can walk, enjoy yourself and those dustbins there is whatever you require. So that will make sure we do. Segeira. Creative spaces. Now let me explain. I think this answers two of the people's questions. Today, if Jezi was to come to Kenya at a performance, Kazaran, their acoustics, the, you know, Beyonce. So we have a program, a project that we're doing. What is currently Green Park Tanya in town? So no Green Park. I say it on citizen level if anyone watched in JKL. And I think I'll start a podcast soon. So I think you guys can be watching me. I'll start a podcast. Who can help me do that? Yeah, read up. In this idea. Apu? You can set me up something else where I can be. Okay. So you've said this is the highest real estate in Nairobi. The most expensive. That didn't be. It's beautiful. It's right next to town. The iconic buildings. Uburupak is on one side. Next to it is a golf course. It was buried to a bus stop. So I've changed that. And now we're getting investors coming in. Last week you remember the Jalizia bus stop saying if you had a restaurant, food court, where people can get food from every country. 50 countries or so it will be full throughout for that cuisine. So out of the designs, we're doing hotel towers but a convention center. But you can have a proper sound auditorium theater, 10,000 capacity meeting, 20,000 performance venues that are affordable, accessible. So imagine some of the towns from Maju, Wunankwa Airport, have you made them now an exit from the expressway there? Exite kungiatao? To say akuna, you have to go to museum okamu.capital center. So we're doing an exit of the expressway there but you get into that Nairobi convention center and we'll clear that space. On top of that, because we can clear all the spaces we want to incentivize the private sector if you're doing a huge development, if you provide for the creative economy, if you provide for playgrounds we incentivize you, we touch you less, we touch you less. I think that can help more people can do that whether that's what we are doing. Now Kulem Tani, what you've agreed with the MCS because MCS runs across the budget is to make sure that in every sub county five words come together there must be a place where there's a studio, there's a small place where people can perform, it's accessible, you don't touch commercial rates and you're able to do it. That one we've put even in our budgets for us to be able to do it. Many guys have talent but how is your foot? When the studio you can record when they know these big guys, you can't afford it but the talent is there. So even in informal settlements, we want to put those now creative spaces for production. Not everybody will buy a mixer, not everybody has a guitar, not everybody has instruments. That's something we are doing and I think once we structure this engagement and this teams, then we know how you guys plug in because then you know you don't need all this equipment for this level of production. Now we have more contests and competitions so our talent comes up. When we see talent that is bankable, we will support them and we will pay for an album, pay for a video shoot, pay for because of that investment is needed. Currently corporates have not been able to come into the creative space because they have not been incentivized and that's at the national level. So we will do our part when it comes and comes to that. You have anything on that? I'll start with that one for the funding bit in terms of identifying talent and then supporting it. So recently at Cabinet we passed the festival fund that will allow us to have some flexibility in terms of how we use our money for artists. So the engagement has always been we would like to support you as county we tried to see how we can give you the best environment to if you're doing a gig how best we support you but we couldn't support you financially because there's no legal framework for it. So ideally what we did is we would give you an ambulance or we would give you a firetrap which is a requirement that you should have if there's advertisement that you would do that you would require to pay some sort of fees to the county we would waver that for you to reduce your costs but now moving forward there's now a structure that we can be able to actually give some sort of sponsorship or we can jointly go into some sort of venture that would make money for both of us. So now we have a structure for that moving forward so in fact now when we do those competitions and we have a fund that we can actually support the artists with the money to do what they need to do. Do I go into that with the details that I wanted? All the things I've covered so we'll go into the details. Yes, all the things you've covered. So you have with us Luta and Cigars. Yes. So in terms of customer service and how you can get in touch with us so both touched on a few things but I just want to emphasize so we're going to set up we're setting up a court line which will have different ways you can access different things in the county so instead of looking for somebody or getting so many different numbers to call the county you will have just one and then whatever your request is it will be directed to the right person. So we're even setting up a call centre for people who will actually demand that and make sure that you you get in touch with whoever you need to. And they have to get back to you if they don't I will not. Yes. So that escalation IT is helping us. If something is there it's still red none I responded to I know who must answer to it. Yes.  Yes. So in addition to the call centre also the system that will allow us to track we will also have that main ruby app which you mentioned briefly so we worked to develop something that you can have access also now on an app be it payments be it queries about specific parts of our sectors of our of our county so whether you have you want to pay your land rates you want to pay for parking you want to consult do I need what kind of license do I need for this specific business all that information will be on the app through we are working with SafariComp to make sure that is done but also it has that component of top to Sacaja. So we've put it as a general thing for now while we see what kind of queries or comments or suggestions that we get and then we will keep modifying it as we go along so we will know that okay these are proposals for partnerships with counties the more we see which which kind of proposals we are getting then we will segment them by sector so maybe this is a health proposal maybe this is a finance proposal maybe this is a sports proposal so we will continue to modify it as we go along but for now it is a general one and you can download the app actually it's on your Apple store


Everybody forced here up in 2023 black football six box half-haze number three pick your team We've got Adam R with the Texans Ravens and the Panthers Ben S. Browns Blair B. Chiefs Caesar with the Bengals Daniel L. Bills Diego Raiders Isaac with the Cardinals Isiah Niners Jack P Vikings Joey Y. Dolphins John P. Seahawks Jose S. Rams Joshua W. Packers Kevin W. Patriots Lee Broncos Luis with the Falcons in the Colts Mark has the Jags Matthew G. Titans Nicholas S. Giants Nicholas O. Lyons Peter B Eagles Robert K. Steelers Ron A. Bears Rory C. Saints Sean O. Cowboys Sean B. Washington Talun H with the Bucks Tim D. Jetson Zach O. with the Chargers. Good luck, everybody Lane is live on fanatics right now. He's got plenty of teams left and fanatics live guys plenty of black football teams left I know we're really close to selling out daytime here and even at night We're gonna want to go to app dot fanatics dot live Uh to the lane sports card shop and check out over there plenty of teams left as well as some bowman chrome Well, Lane's over there killing it right now I'm just gonna get you guys the link here I if they did it last year But this year I feel like if there's a team in the nl that can beat the Braves It's the Phillies because of just the don't give a don't give a crap like attitude and like I they have the mental capacity to beat them I don't think that'll happen this year, but they have that like That like we can beat anybody mentality The only thing is is that the Braves is just like a runaway train That's the problem with the Braves here. Is there like too good? I don't think it happens, but I don't think the Dodgers can beat the Braves but I think the Phillies just like I say you you take one in Atlanta, then you have games at home and like that's That's exactly what happened last time You get on that you get on that momentum when they kind of just go. Hey, there we go a Chan rookie orange To 25 This guy is an end zone magnet All he knows how to do there's a ding on the corner. I'm gonna send a boxing wrapper with the uh a chan here Very nice orange color match. So we got Tillman rookie for the for the brown speed. I do. I think the Braves are world go to the world series and uh Al I don't know. I don't know about the al that one's more interesting to me. Yeah Dual patch is will lavis and hendon hooker to 50 a couple of uh, I think hooker was second round, right? So I think that's a couple second round cute Or maybe hooker was later. I forget um I assume it's different people here. I have these we'll random we'll random that in just a moment or at the end of the break here So Detroit is Nicholas. Oh, so yeah, Nicholas only had the one spot Yep, we'll random that at the end. Good luck on that one. It's a cool working dual patch Quinn and Williams wow midnight signatures to 99 and on card Quinn and Williams Dude What do you guys like more of the the smoke show or the midnight? Holy crap, that's awesome.  I don't like the midnight more as well. I'll like this. Yeah I want them both but yeah Um, I feel like puka has had cards somewhere NFL uniform it might be though Does any can anybody think off the top of how puka has had other NFL? He he was in I he was in some collegiate products if I remember correctly Yeah, he was with like relics or something. I can't remember 100% he I know we pulled his cards before But NFL uni this might be the first one acres to 75 rams Look at that. It's viking scholar match on the purple Desmond Ritter falcons base It's like a bear coming out of the woods. Yeah, he's pretty comparable to a bear as well. He's Freaking he's huge dude dual jersey. Wow another one of these will Anderson and Tyree Wilson to 150 who both look very good by the way Yeah, this class overall, it's like a very solid classic like above average I'd say Even the late second round picks are are even turning out to be dusk to dawn. I see now dusk to dawn Uh, we're in and that at the end make sure you Run them to the side musgrave rookie auto to 199 for the Packers Musgrave rookie auto Packers and Packers again. We've got laundry tag sizable signatures three of five Sean Clifford Packers very very nice both autos in this one sick green color match at that Pretty cut pretty card. There you go three of five on the laundry tag Clifford quarterback action there Never a bad time to get a Rookie quarterback laundry tag auto You never know Never know man Vanta sp Tyreek hill Guys, I'm trying to get the the right light on this. These look better in person though That's Vanta sp Tyreek hill Holy cow They did they did really well with the designs on mostly every single card in this set this year That's a 35 is George Kittle for the Niners Shrey Tucker Raiders rookie jersey to 150 You think so Philly? Hey rookie kicker out of the 50 Jake moody Seems pretty good. I mean Some of my fantasy he's he's making feel I mean he's making most of the kicks, right? Jake moody rookie auto and I mean if he's rookie kicker He must have been drafted pretty highly and a smith and jigba dual patch rookie out of the 50 seattle Yeah, that's what I'm trying to think steven. I think he was in something before I just can't put my Come up with my finger on it what puka was in Nice smith and jigba That's a fun product dude. This is It's more thick easier. We got some nice cards coming up then Justin shorted to 75 bills rookie Deuce Vaughn on the rookie for dallas Quentin Johnston a rookie jersey to 150 for the chargers Yeah, I guess that's the one thing is it's still bringing the silver background. Some of the cards looks looks good though It looks like a black background Nice sizable signatures veteran here Kenneth walker the third seahawks four of five four plus five is nine, which is his jersey number Green is basically a color match as well Great break for the seahawks nice k9. He's very good Right. Yeah, so I'm trying to think nfl uni For puka think it's his first nfl uni. He's been in stuff before though Got a tank big speed rookie dual patch auto to 75 for the jags You want to give me thick and pincers? I can start leaving some of this stuff How much pressure in the bruise? I mean a decent like yeah, it's a close out game, but especially since you're going up against gallon Especially you have to take good at bats from the get-go.  Gino seahawks break continues here. It seems like Gabriel Davis On the base there rushy rice ricky jersey going out to the chiefs to 150 rookie influx Chargers there we go nine of ten rookie auto quentin johnston Very nice hit chargers hoping he can step up He's got some talent I think he's still what third on the depth chart behind uh, really without my key It should be palmer in front of him. I would think I don't know though With rookie receiver sometimes takes a minute, but like they ascend quicker sometimes with the depth chart Nice quentin johnston, and we got rushy rice dual patrick. You got it to 99 for the chiefs Yeah, corb corbin was good Just didn't get the run support As far as like pressure on the brewers, I don't know if it's like a ton like no one expects them to go like super far no Really? Which is unfortunate But they did win like I wouldn't say the worst division but The worst division in the nl's the worst. Yeah, one of the worst the only one that's worth a l central and that's That's saying something the cubs are good But yeah, but reds were solid. So that's why I mean a l central is definitely worse. I'll say that They were just the most consistent team in that division 25 clay pool for the bears But so there's so there's another good matchups today. That's the cool thing about the the smaller series is like You know someone wins a game the next day. It's an elimination game and it's like oh boy like So everyone with their backs against the wall or even if you're trying to win is going to treat it like it's like okay We got to get it done Like short leash on the pitchers and pinch hit and whoo force field short range Jalen Hyatt Dude, yeah, you guys have go to spencer's gifts and you see the the orbs that have the yeah, that's what that is That's exactly what that is right there Go to the back of spencer's gifts all the black lights and stuff back in the day I guess they still exist in some places. I don't know. I've been in them all in a while like that though force field Short print is rookie Jalen Hyatt for the Giants Another dual dude. What is up with the duals in this one dusk to dawn concade and mayor to 150 bills raiders Trevor Lawrence sizable signatures. What a five patch auto jags Oh Baby mark a with the Jacksonville Jaguars a monster trevor Lawrence Patch auto and the sizable sigs Holy cow with the number patch. Yep Vaughn's leader damn There's bangers in every half case we do a rookie patch auto to 50 orange color match bears tyler scott And there we go So, yeah, this silver is interesting on some of them But the true rpa style of black like this one. It looks very good on i'll say Not the cleanest sigs, but it's just those thicker I guess they're almost like markers that they have amused for the for the silver You need to get something where they have those blue point pens that they always sign with but with the With the silver and white the golden stuff. So all right. We have a few multi random to do Um, I'll check and make sure that we even have to do them Uh, let's see bill's raiders Raiders is Diego bills Stanley up Houston and vegas Houston is atom are And then the lab isn't hooked there as well. All right three randoms Didn't see any of these first case. Of course, we see three of them in the next half case Sometimes that's how it goes that's how it went in collegiate Only the titans left in the uh In the fanatics Penini black it's the first half case. Yep So yeah guys lane is live on fanatics live get on over there and get some teams There's a lot more teams left over on fanatics live. They're right here now That's the place to be if you're looking for uh More options. There's also a bowman chrome hobby going on over there today So three randoms here triple relics or not. Sorry. I typed in triple on the thing It's only the title same but anyway dual relics levis hooker titans lions Anderson and tyree Wilson tactons raiders and then bill's raiders was mayor concade So good luck on these Nine on each whichever one's up top. We'll get them Um At tight little triple relic. We know we know it's not bad. We'll just do it nine times here on everything one two three four five six seven eight and nine the titans So that was the quarterback one nine times on the wilson and anderson one two three four five six seven eight and nine the texans are up top And then the ricketyte ends here one two three four five six seven eight and nine bills All right, let's recap Other fun break So we had the force field. I'm sure that show those rocks again. Um bill's got that one The texans got this one and the titans got the quarterbacks force field short print jalen hyatt for the giants relics, uh, rushy rice tray tucker Quentin johnston autos now luke musgrave Equinny williams midnight signatures super super clean on card auto great design as well Or the jets on that one relic auto rushy rice tank bigsby tank bigsby again jack's crush the spring jake moody tyler scott jackson smith and jigba Quentin johnston to ten He had four or five kenneth walker the third. That's a fantastic hit and the schclifford laundry tag three of five patrick He auto for the packers And then we had vanta sp tyreek hill great-looking card there And sizable signatures one of five for the jaguars trevor lorence That hit was the big hit that time. Thanks again everybody on the half case number four