Evaluate the proof of the following result.Result Let x, y Zand let a and b be odd
Chapter 3, Problem 3.57(choose chapter or problem)
Evaluate the proof of the following result.Result Let x, y Zand let a and b be odd integers. If ax + by is even, then x and y are of the same parity.Proof Assume that x and y are of opposite parity. Then x = 2p and y = 2q + 1 for someintegers p and q. Since a and b are odd integers, a = 2r + 1 and b = 2s + 1 for integers r and s. Henceax + by = (2r + 1)(2p) + (2s + 1)(2q + 1)= 4pr + 2p + 4qs + 2s + 2q + 1= 2(2pr + p + 2qs + s + q) + 1.Since 2pr + p + 2qs + s + q is an integer, ax + by is odd.
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