Below is given a proof of a result. What result is being provedProof Assume that x is
Chapter 3, Problem 3.38(choose chapter or problem)
Below is given a proof of a result. What result is being proved?Proof Assume that x is even. Then x = 2a for some integer a. So3x 2 4x 5 = 3(2a)2 4(2a) 5 = 12a2 8a 5 = 2(6a2 4a 3) + 1.Since 6a2 4a 3 is an integer, 3x 2 4x 5 is odd.For the converse, assume that x is odd. So x = 2b + 1, where b Z. Therefore,3x 2 4x 5 = 3(2b + 1)2 4(2b + 1) 5 = 3(4b2 + 4b + 1) 8b 4 5= 12b2 + 4b 6 = 2(6b2 + 2b 3).Since 6b2 + 2b 3 is an integer, 3x 2 4x 5 is even.
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