I think I might be beginning to wrap my head around some simpler proofs, but I'm a little stumped on this one from my textbook:
Use a direct proof to show that if two integers have opposite parity, then their product is even.
If I have integers $(m,n)$ with even parity, I would then have (from what I've gathered) an integer $a = 2m$ and an integer $b = 2n$. I'm not sure where I go from here in looking for a product?
In my mind I would do $a \cdot b = (2m)(2n) = ???$
I know I'm dealing with integers, and I use $m$ and $n$ to respectively denote different integer values I'm dealing with.
Can anyone walk me through how to finish this out?