test 2 study guide - Disproof by counterexample Method of...

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Disproof by counterexample Method of generalizing from the generic particular (exhaustion) Method of Direct Proof: 1. Express statement to be proved in the form “Ax E D, if P(x) then Q(x).” (often done mentally) 2. Start proof by supposing x is arbitrary but particular element of D for which the hypothesis P(x) is true. (This step is often abbreviated “Suppose x E D and P(x).”) 3. Show that the conclusion Q(x) is true by using definitions, previously established results and rules of logical inference D | n => n=dk (d divides n) N is a multiple of d, d is a factor of n, d is a divisor of n QTR: n=dq+r and 0 <= r < d where n and d are integers and q and r are unique integers Method of proof by contradiction: 1. Suppose the statement to be proved is false. That is, suppose that the negation of the statement is true 2. Show that this supposition leads logically to a contradiction 3. Conclude that the statement to be proved is true Method of Proof by contraposition 1. Express the statement to be proved in the form Ax in D, if P(x) then Q(x) (mentally)
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This note was uploaded on 04/27/2008 for the course M 3 taught by Professor Mitra during the Fall '08 term at University of Texas at Austin.

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test 2 study guide - Disproof by counterexample Method of...

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