(a) Let m and n be two integers. Prove that m+ n is even if and only if m and n are of

Chapter 3, Problem 5

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(a) Let m and n be two integers. Prove that m+ n is even if and only if m and n are of the same parity. (b) Let S = {a, b, c, d} be a set of four integers. Prove that if m pairs of distinct integers of S are of the same parity and the remaining n pairs of distinct integers of S are of opposite parity, then m and n are of the same parity.

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