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 TOPICS This page:   logic    Search   Dr. Math See also the Dr. Math FAQ:   false proofs,   classic fallacies and   liars, truthtellers and   proofs Internet Library:   logic HIGH SCHOOL About Math Analysis Algebra    basic algebra    equations/graphs/      translations    linear algebra    linear equations    polynomials Calculus Complex Numbers Calculators/    Computers Definitions Discrete Math    permutations/    combinations Exponents    Logarithms Fibonacci Sequence/   Golden Ratio Fractals Functions Geometry    Euclidean/plane      conic sections/        circles      constructions      coordinate plane      triangles/polygons    higher-dimensional      polyhedra    non-Euclidean    practical geometry    symmetry/tessellations History/Biography Interest Logic Negative Numbers Number Theory Physics/Chemistry Probability Projects Puzzles Sequences/Series Sets Square/Cube Roots Statistics Transcendental   Numbers Trigonometry Browse High School Logic Stars indicate particularly interesting answers or good places to begin browsing. Selected answers to common questions:     Venn diagrams. 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>? Five-Set Venn Diagram? [11/25/2001] What does a five-set Venn diagram look like? Football Logic: Who Defeated Whom...? [8/17/1996] Four teams were brown, blue, red, and purple; the competing captains were Albie, Barry, Bill, and Ben... who defeated whom? The Four Doors of Xanth [02/11/1998] Each door conceals one item: a treasure, a rope, a key, and a lantern. You must find all four items in a particular order to keep the treasure. Fuzzy Logic [04/26/1997] What is fuzzy logic? Game Theory and Payoff Matrices [11/14/1998] Can you give me a good introduction to game theory? What is a payoff matrix? Gauss' Method for Solving Equations [12/11/1998] How do you use Gauss' method and matrices to solve systems of equations? Why does this method work? A Geometry and a Logic Problem [3/11/1995] Problem 1: A cylindrical hole six inches long is drilled straight through the center of a solid sphere. What is the volume remaining in the sphere? Problem 2: The classical stay-switch problem. Geometry Puzzles [12/18/1995] A student asks Dr. Math for help in finding the correct combinations of numbers to solve two puzzles. Godel's Incompleteness Theorem [01/18/1999] What does Goedel prove in his incompleteness theorem? Goedel's Incompleteness Theorem [08/08/1997] How did Goedel prove that any nontrivial logical system cannot be proven to be inconsistent? History of the Symbol for "Therefore" [11/14/2005] Why is it that the symbol for "therefore" is a centered dot with two lower dots? Where did that symbol come from? How Can a Set Be Empty? [09/29/2003] Why is the empty or null set called a set when it has no elements? How Many are in the Group? [10/17/1996] Everyone in the group had been to at least one of the parks... How Many Pieces of Candy in Each Jar? [09/30/1997] At the annual Cumberland County fair, one of the more popular booths is the Candy Contest... A Hundred Thousand Switches, One Defect: How Few Tests? [04/19/2011] Seeking to minimize the binary tests necessary to identify a manufacturing defect, a student imagines representing the problem as a two-dimensional array, and pursuing that strategy into higher dimensions. Doctor Anthony introduces a bit-wise approach for determining the least number, then proceeds through a smaller example to demonstrate the general method for solving such problems of efficiently identifying the one bad apple. If It Doesn't Follow a Form, Don't Draw a Conclusion [09/22/2011] A student of syllogisms and detachments struggles with statements that do not map to those forms. By rhetorically extending her examples, Doctor Peterson reveals that sometimes, the only thing you can conclude is "No conclusion possible." If P then Q [08/29/1997] I don't understand how if p is false then regardless of q the statement is true. Implications in Logic [10/29/2002] I don't understand the first four rules to do with implications: Modus Ponens, Modus Tollens, Hypothetical Syllogism, and Disjunctive Syllogism. Inclusion-Exclusion Principle [09/03/2002] In a survey of 100 people, 85 like calypso and 93 like pan. Calculate the number of people who like both calyso and pan. The Indeterminate Nature of 0/0 [12/21/2000] I have a theory that 0/0 = any number, and is not "indeterminate" as is traditionally claimed. Can you explain the flaw in my thinking, and the "indeterminate" nature of 0/0? Indirect Proof of Parallel Lines [11/26/2001] I have asked my high school geometry class to prove indirectly that parallel lines have the same slope. Unfortunately, I cannot figure out how to do it myself... Indirect Proofs [09/21/1997] If Clark is a mathemagician, then Lois is his assistant... Induction Proof with Inequalities [07/03/2001] Prove by induction that (1 + x)^n >= (1 + nx), where n is a non- negative integer. Inductive Misunderstanding [04/26/2012] One explanation of mathematical induction leads a student to question the method's validity; a second makes him doubt its purpose. Doctor Rick re-lays the groundwork for logic's "infinite staircase." Inductive vs. Deductive Reasoning [07/24/2001] Can you explain the difference between inductive and deductive reasoning? Infinite and Transfinite Numbers [5/28/1996] Can anyone explain to me, in a simple way, what transfinite numbers are and how they're different from infinite numbers? Infinite Sets [09/24/1997] In my algebra class we have been debating whether the integers or the whole numbers contain more elements... Integer Logic Puzzle [04/22/2001] Two integers, m and n, each between 2 and 100 inclusive, have been chosen. The product is given to mathematician X and the sum to mathematician Y... find the integers. Interchanging Variables in Logic [04/10/2003] What are the four rules of logic? Can the variables (p and q) be interchanged? Why or why not? Interpreting Intersections [07/09/2002] Out of 100 people, 10 drink Coke, 15 drink Sprite, and 20 drink Pepsi. How many drink both Coke and Pepsi at the same time? Coke and Sprite? Pepsi and Sprite? All three? Introduction to Logic and Truth Tables [09/27/2000] I can't figure out the p and q thing. Can you explain what they are and how operations like "AND" work? Invalid Logic Argument [9/9/1996] If I want the result to be true but the premise is false, the argument will be invalid... Is Henry Guilty? (Geometry Puzzle) [6/10/1996] In Hughmoar County, residents shall be allowed to build a straight road between two homes as long as the new road is not perpendicular to any existing county road... Is It Possible That x/0 is Not Really Undefined? [06/14/2004] Is it possible that 1/0 is not really undefined, but is in fact the key to a whole new class of numbers, much as the imaginary unit i led to the development of complex numbers? John Venn and Venn Diagrams [09/04/1998] Can you give me some information on John Venn and the origin of Venn diagrams? Karnaugh Maps [05/07/2000] What are Karnaugh maps? How are they used? Knowing People at a Party [08/27/1998] Prove that at any party, there are two people who know the same number of people. Assume that if A knows B, then B knows A. Assume also that everyone knows himself or herself... Largest x, x^2 less than 2 [10/23/1999] Prove that there is no largest real number x, such that x^2 is less than 2. (Use indirect proof.) Lewis Carroll's Logic Problems [01/15/1997] Where can I find out more about Lewis Carroll's logic problems? Page: []

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