Is this proof correct or not? If the proposition is false give a counter example AND state what was done wrong in the proof. If this proposition but poorly written then improve the proof. If this proof is well written then tell me.

Proposition: for all integers, m and n, if mn is an even integer then m is even or n is even.

Proof. For either m or n to be even, there exists an integer k such that m = 2k or n = 2k. So if we multiply m and n then the product will contain a factor of 2 so mn will be even.