The problem with trying a direct proof is that it will be hard to separate \(a\) and \(b\) from knowing something about \(a+b\text{.}\) On the other hand, if we know something about \(a\) and \(b\) separately, then combining them might give us information about \(a+b\text{.}\) The contrapositive of the statement we are trying to prove is: for all integers \(a\) and \(b\text{,}\) if \(a\) and \(b\) are even, then \(a+b\) is even. Thus our proof will have the following format:
in-context