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?
how can i prove this using contraposition?
Answers
Steve
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.
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.