Prove the following statements using direct, contrapositive, or contradiction proof. a. Suppose x is an integer. Then x is odd if and only if 3x + 6 is odd. b. Suppose a, and b are integers. Prove that a is equivalent to b(mod 10) if and only if a is equivalent to b(mod 2) and a is equivalent to b (mod 5). c. If a is an integer, then a^3 is equivalent to a(mod 3). d. There exists an integer n for which 11 | [(2^n) - 1].

Prove the following statements using direct, contrapositive, or contradiction proof. a. Suppose x is an integer. Then x is odd if and only if 3x + 6 is odd. b. Suppose a, and b are integers. Prove that a is equivalent to b(mod 10) if and only if a is equivalent to b(mod 2) and a is equivalent to b (mod 5). c. If a is an integer, then a^3 is equivalent to a(mod 3). d. There exists an integer n for which 11 | [(2^n) - 1].

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter1: Fundamental Concepts Of Algebra

Section1.2: Exponents And Radicals

Problem 85E

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