Question

If m and n are integers such that mn is even, then m is even or n is even.

how can i prove this using contraposition?

Answer 1

if both are odd, we can let

m = 2a+1
n = 2b+1

mn = (2a+1)(2b+1) = 4ab+2a+2b<b>+1</b>
so, mn is odd if m and n are both odd.

So, if mn is even, then m and n cannot both be odd.