must be proved using contradiction.

Question

For all integers m and n, if m*n is odd, then m is odd and n is odd. (Hint: you'll need two cases in your proof)

Answer 1

Assume that (without loss of generality) m is even. Then m=2k for some integer k. But then mn=2kn=2(kn) which means that mn is even. This gives a contradiction. So m can not be even. In the same way, n can not be even and the proof is complete.