Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN: 9781133382119
Author: Swokowski
Publisher: Cengage
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Question
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].
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