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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. 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 1000-mile 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 lower-level 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(n-1))^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>? Page: []

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