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Browse High School Logic
Stars indicate particularly interesting answers or
good places to begin browsing.
Selected answers to common questions:
Venn diagrams.
 Claim the Last Flag [10/25/2002]

Two teams face 21 flags. Teams take turns choosing 1, 2, or 3 flags at
each turn. The team that can claim the last flag wins.
 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]

Can you tell me the meaning of the following logical operations: AND, OR,
XOR, NAND, NOR, NOT?
 Concept of Farmer Crossing a River [04/30/2002]

What concept does the farmer, fox, and chicken problem use, and how
does it relate to the sheriffs and outlaws problem, husband and wives
problem, and missionaries and cannibals problem?
 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)?
 Context, Language, and False Equations [02/12/2001]

Is there such a thing as a false equation? How does the context in which
it is set affect the truth of an equation?
 Contrapositive [02/27/2002]

Am I allowed to say my reason is the inverse?
 Contrapositives and Monotonic Functions [03/17/2003]

Defining 'monotonic' (increasing or decreasing functions) and
'contrapositive'.
 Converse, Inverse, Contrapositive [09/08/2001]

Write the converse, inverse, and contrapositive of each conditional and
determine whether they are true or false; if false, give a
counterexample.
 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]

A challenging logic problem involving five criminals charged with five
crimes. The names of the criminals are the same as the crimes, but no
criminal commited the crime of his name. Using several clues,
determine who committed murder.
 Crossing the Desert [05/22/2001]

A truck gets one mile per gallon, and can hold 400 gallons at a time. How
much is the minimum amount to cross a 1000mile desert?
 Deductive Reasoning [09/21/2000]

What is deductive reasoning? How do you use it?
 Defining Multiplication [08/16/2002]

What is the distinction between 3*4 and 4*3?
 De Morgan's Laws [09/21/2000]

What is "De Morgan's Law"?
 Deriving Properties of Fractions [08/10/2003]

Derive the rule for multiplying fractions, that a/b x c/d = ac/bd,
using lowerlevel properties of multiplication and rational numbers.
 Diagram for Math Numbers [10/05/1997]

My daughter is doing a tree diagram using terms related to math
"numbers." Could you please explain in lay terms what surds are?
 The Difference between And and Or [01/23/2008]

There are 3 knives, 4 spoons, and 4 forks on a table. What fraction of
the utensils are spoons OR forks? I think it should be 4/11 but the
answer is 8/11. Can you explain why?
 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.
 Distributing 'Not' over a Conjunction [09/18/2003]

When 'It is not true that...' appears in front of a conjunction, does
it apply to both conjuncts, or only the first one?
 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]

What kind of logic statement is "I am telling you the truth when I say I am a liar"?
 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]

This proof is giving me major problems: F(2n) = (F(n))^2 + (F(n1))^2.
...
 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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