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Browse High School Logic
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Selected answers to common questions:
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Claim the Last Flag [10/25/2002]

Closed Sets [02/27/1999]
Is a union of finite number of closed sets and the intersection of any number of closed sets closed?

Coat Confusion [03/20/1998]
When the fire alarm went off, 6 people in a room each grabbed a coat, but no one took his own. Who took A's coat?

Computers: Defining Logical Operations [05/21/1998]


Conjunctive and Disjunctive Normal Forms [09/25/2000]
How can I find the conjunctive normal form (CNF) of an expression from the disjunctive normal form (DNF)?

Constructing Truth Tables [11/03/2000]
How can you make a truth table for the expression pv(p^~q)?

Constructing Truth Tables [02/17/2006]
Construct a truth table for the statement ~q v (p^r).

Constructing Truth Tables for More Than Three Statements [03/07/2004]
I know how to do truth tables for up to three statements. How do I continue with a fourth or fifth statement such as (p ^ q) -> (rvs)?


Contrapositive [02/27/2002]
Am I allowed to say my reason is the inverse?

Contrapositives and Monotonic Functions [03/17/2003]

Converse, Inverse, Contrapositive [09/08/2001]

Converse of the Pythagorean Theorem [02/14/2003]
What is the converse of the Pythagorean theorem?

Countability of Primes and Composites [05/18/2002]
If the union of two sets is countable, can either of the sets be uncountable?

Countable Sets and Measure Zero [05/12/2001]
How would you prove that if a set S is countable, then S has measure zero?

Criminal Logic Problem [02/19/2005]

Crossing the Desert [05/22/2001]

Deductive Reasoning [09/21/2000]
What is deductive reasoning? How do you use it?

Defining Multiplication [08/16/2002]

De Morgan's Laws [09/21/2000]
What is "De Morgan's Law"?

Deriving Properties of Fractions [08/10/2003]

Diagram for Math Numbers [10/05/1997]


Difference between If...then and Suppose...then [11/25/2002]
What is the difference between 'If X, Then Y' and 'Suppose X. Then Y.'? X and Y are given statements used in proving something.

The Difference between Open Sentences and Statements [06/28/2008]
If an open sentence is always true for all values of the variable(s) in it, is it still an open sentence or is it considered a statement?

Disjunctive Syllogism [09/25/1998]
What is the Disjunctive Syllogism?

Disorderly Deduction [09/23/2011]
A student of syllogisms gets thrown by statements that seem out of order. She and Doctor Peterson discuss biconditionality, canceling, plumbing -- even gibberish -- until order and letters give way to the more fundamental substrate of logic: relationships.


Divisor Proof with Contrapositive [09/16/2002]
I have been trying to prove that if n^2 divides m^2, then n divides m.

Domain, Parentheses, and Brackets [11/01/2001]
Translate: All people who are not poor and are smart are happy. Those people who read are not stupid. Jill can read and is wealthy. John is poor and stupid. Happy people have exciting lives....

Equivalence Relations [12/10/2001]
Let X={1,2,3,4,5}, Y={3,4}. Define a relation R on the power set of X by A R B if A U Y = B U Y. Prove that R is an equivalence relation. What is the equivalence class of {1, 2}? How many equivalence classes are there?

Estimation and Fermi Questions [04/10/2002]
I'm currently learning about Estimation techniques similar to those used by the famous scientist Enrico Fermi, who proposed the question, 'How many piano tuners are there in Chicago?'

Examples of Logical Paradoxes [03/14/2006]

Exclusive or Inclusive Disjunction? [06/28/2001]
I have difficulty interpreting this problem, especially the first sentence: Tanya is either a singer or a ballerina...

Explaining Mathematical Induction [08/29/1998]
What is mathematical induction? I have to do a report on it.

Explain Supremum [02/02/1998]
Can you please explain, perhaps with an example, the concept of "supremum"?

Fibonacci Proof [01/29/2001]

Finding the Operation [06/21/1999]
How can I find the operation '?' given 3?4 = 5, 4?7 = 1, 8?4 = 0, and 1?2 = 9?

Finding the Power Set of a Power Set [02/17/2005]
What is "the second power set", or the power set of the power set of a set, say set <1,2,3>?


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