What result is being proved below, and what procedure is being used to verify the
Chapter 3, Problem 3.43(choose chapter or problem)
What result is being proved below, and what procedure is being used to verify the result?First, we present the following proof.Proof Assume that x is even. Then x = 2a for some integer a. Thus7x 3 = 7(2a) 3 = 14a 3 = 14a 4 + 1 = 2(7a 2) + 1.Since 7a 2 is an integer, 7x 3 is odd.We are now prepared to prove our main result.Proof Assume that 7x 3 is even. From the result above, x is odd. So x = 2b + 1 for some integer b. Thus3x + 8 = 3(2b + 1) + 8 = 6b + 11 = 2(3b + 5) + 1.Since 3b + 5 is an integer, 3x + 8 is odd.
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