Define E to be the set of even integers; E = {$x$ $\in$ $\mathbb{Z}$ : $x$ = 2$k$, where $k$ $\in$ $\mathbb{Z}$}.
Define F to be the set of integers that can be expressed as the sum of two odd numbers.
Prove E = F.
My attempt: The only way I can figure out the solution is by providing numbers and examples. It's easy to see that two odd numbers will always equal an even integer. I just don't know how to write the proof for it.
Best Answer
Hint: $2k = (2k - 1) + 1$.
$1$ is an odd number. Is $2k-1$ odd? Even? (Both? neither? impossible to tell?)