Evaluate the proof of the following result. Result Let x, y. epsilon Z and 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 some integers p and q. Since a and b are odd integers, a = 2r + 1 and b = 2s + 1 for integers r and s. Hence ax + by = (2r + 1)(2 p) + (2s + 1)(2q + 1) = 4pr + 2 p + 4qs + 2s + 2q + 1 = 2(2 pr + p + 2qs + s + q) + 1. Since 2pr + p + 2qs + s + q is an integer, ax + by is odd