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