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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.



About Fuzzy Logic [05/06/2003]
What is fuzzy logic? What's the difference between fuzzy logic and Boolean logic?

Cantor, Peano, Natural Numbers, and Infinity [03/19/1998]
A conversation on transfinite numbers and contradictions the questioner believes exist in Cantor's paper introducing the diagonal method.

Contrapositive, Converse, Inverse [06/10/1999]
How can I write the contrapositive, converse, and inverse of and prove or disprove the statement, "If m + n is even, then m and n are even"?

Derfs and Enajs: Algebra and Venn Diagrams [03/09/2003]
All Derfs are Enajs. One-third of all Enajs are Derfs. Half of all Sivads are Enajs. One Sivad is a Derf. Eight Sivads are Enajs. The number of Enajs is 90. How many Enajs are neither Derfs nor Sivads?

A False Statement Implies Any Statement [09/25/1997]
Do you know any ways to make learning and remembering quantifiers and laws of inference easier?

Finding One Coin of 12 in 3 Steps [8/6/1996]
Given a pile of twelve coins of equal size with one of a different weight, in three weighings find the unequal coin...

Inductive and Deductive Examples [11/21/2001]
Solve by deduction and then induction: Bob wants to figure out what his teacher wants for his birthday, but he cannot ask his teacher directly. How does he pick the perfect present?

Intersection of Sets [10/02/2000]
I do not understand intersection of sets. Can you give me an example?

Lines, Points, and Infinities [09/01/2001]
What is the cardinality of the set of real numbers between 0 and 1? Is this cardinality less than, greater than, or equal to the cardinality of real numbers between 0 and 2?

Logic: Definitions [04/04/2000]
What does deductive reasoning mean? What does inductive reasoning mean?

Logic of Indirect Proofs [10/16/1996]
Can you explain the logic of indirect proofs?

Lucky Seven Fractions Puzzle [12/22/2001]
Put numbers 1-9 in order to make the equation correct: XX/XXX+XX/XX=7.

Main Connectives in a Proof [10/28/2001]
Focusing on the main logical symbols in a proof.

Probability: Let's Make a Deal [4/29/1996]
Should the contestant stick with the original choice of doors or switch and choose the other door? What about the lottery?

Properties and Postulates [08/04/1999]
How do you discover or create a property? What is the difference between a property and a postulate? Do we have to prove all properties?

The Sportsville Teams [10/30/1997]
Are there straightforward methods for solving logic problems?

Truth Tables and Computer Circuits [01/17/2000]
Can you please explain how to read and draw computer circuit diagrams, how to form truth tables from reading the diagrams, and the logical arguments behind this?

The Truth-teller, the Liar, and Ambiguous [7/9/1996]
God knows everything and always replies the truth. The devil knows everything, but always lies. The third person's answers are completely useless and could be right or wrong. Using three questions, determine who is who.

What is Fuzzy Logic? [10/29/2000]
I need a simple definition of fuzzy logic and what it's used for.

Where and with What Weapon Was Each Man Murdered? [09/19/2001]
One rainy evening, five military men were murdered in the old mansion on Willow Lane... use the clues to make a grid and find who was murdered with what weapon, and where.

Who Owns the Zebra? [08/05/1997]
I have tackled this indirect reasoning problem and have come up with a solution that I am not sure is correct.

Who Stole Second Base? [2/20/1995]
The umpire was convinced that either Archie, Buster, Cal, or Dusty had stolen second base. Each player, in turn, made a statement, but only one of the four statements was true. Who told the truth?

17 and 19 Balls, Colliding [03/25/2003]
How many collisions will occur in the described system?

Absorption Laws [04/10/2001]
Prove x + x'y = x + y, or x + xy = x.

Advanced Topics in Symbolic Logic [10/28/2002]
I cannot find any unsolved proofs that I can just solve for fun.

All People in Canada are the Same Age [01/18/2002]
For n = 1,2,3,..., every bag contains n solid-colored balls of only one color. Prove for n = 1: A bag with one ball clearly has balls of only one color... Find the error in the proof.

Are Different Proofs of a Theorem Really the Same? [07/05/2006]
If you have a mathematical system with several axioms (call them A, B, C, D, E and F), is it possible to have two proofs of a theorem in this system where one proof uses only axioms A, B, and C and the other proof uses only axioms D, E, and F? In other words is it possible for two proofs to use no common axioms? Or are all proofs of that theorem really based on the same set of axioms?

Are They Wearing Seatbelts? [3/26/1995]
80 percent of all California drivers wear seatbelts. If 4 drivers are pulled over, what is the probability that all 4 will be wearing their seatbelts?

Arranging Numbers [06/26/2002]
Arrange the numbers 1-8 into the given configuration such that consecutive numbers are never adjacent.

Basic Truth Tables and Equivalents in Logic [05/23/2000]
What are the truth tables for basic propositional logic operations? What are some useful equivalencies?

Binet's Formula and Induction [11/28/2001]
What is induction? Can you prove Binet's formula by induction?

Boolean Algebra and DeMorgan's Theorems [05/14/2001]
How do I simplify not{not[A and not(B)] or C}?

Boolean Algebra Problems [12/05/1997]
Prove x'y' + x'y + xy' = x' + y'; x'y' + x'y + xy' + xy = Identity.

Boolean Algebra Proofs [09/25/1999]
Prove the Boolean expression ab + bc + ca' = ab + ca'; also, prove using contraposition that 2(q^2) does not equal (p^2) when p and q are relatively prime.

Boolean Numbers [04/01/2003]
Our C Programming course said a Boolean number was a number that was either true or false. I'm not sure what a true or false number is.

Building Sets [05/26/2002]
Is 5 part of the set {x:x is a multiple of 7 and 5 < x < 56}?

Calculating Number of Possible Subsets of a Set [06/14/2002]
What is the formula for calculating the number of posssible subsets for a finite set?

Can Rewriting P -> Q as ~Q -> ~P Lead to a False Conclusion? [01/21/2006]
An interesting logic puzzle about determining a birthday leads to a discussion about interpretation, logic, and seeming confusion when one of the logic statements is rewritten in a different but equivalent form.

Cardinality between Open and Closed Sets [09/20/2001]
I would like to know how to prove that the sets (0,1) and [0,1] have the same cardinality.

Choosing a Random Rational Number [01/23/2001]
0 percent probability should mean that it is impossible for a rational number to be chosen from the set of real numbers, but obviously this isn't the case. How can it be 0 percent probability but not impossible?

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