Question

Prove that for all integers m and n if m and n are even then m+n is even

Answer 1

Use either proof by contrapositives or by contradiction:

Proof by contrapositive:

Assume that it is not true that m + n is even. Then either m or n is odd. Since the addition of an odd and an even number is odd, then m + n is odd.

In this case we show that if either m or n is odd then m + n is not even we prove that if m and n are even, m + n must be even