# Quiz 5 - CSE 260 QUIZ-5 Proofs ANSWER(20 minutes NAME 1 Indicate if the following are trivially true or vacuously true for a real number x and

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CSE 260 QUIZ-5– Proofs - ANSWER (20 minutes) NAME: 1. Indicate if the following are trivially true or vacuously true for a real number x and n=1. (a) If x 0, then (1 + x ) n 1 + nx Trivially true ( p q , the implication is trivially true if q is true; in this case, the truth value of p is irrelevant). (b) If n is even, then x n 0 Vacuously true ( p q , the implication is vacuously true if p is false). 2. Prove that if n is an integer and 3n+2 is odd, then n is odd using (a) an indirect proof. Theorem: (3n+2 is odd) (n is odd) Contrapositive: ¬ (n is odd ) → ¬ (3n+2 is odd) (n is even) (3n+2 is even) n is even. Therefore, by the mathematical deFnition of even n can be written as n=2k for an integer k Therefore, 3n+2=3(2k)+2=2(3k+1) is even becuase 3k+1 is an integer (b) A proof by contradiction. Theorem: (3n+2 is odd) (n is odd) Assume that the theorem is false, i.e., for all integers n ¬ ((3n+2 is odd ) (n is odd)) ⇔ ¬ ( ¬ (3n+2 is odd)

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## This note was uploaded on 03/30/2008 for the course CSE 260 taught by Professor Saktipramanik during the Spring '08 term at Michigan State University.

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Quiz 5 - CSE 260 QUIZ-5 Proofs ANSWER(20 minutes NAME 1 Indicate if the following are trivially true or vacuously true for a real number x and

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