Suppose is not allways even (contraposition): Then ther exists a number such that is odd.

Now fill in n= 2k+1 (odd number) and n = 2k (even number) to show this can not be the case.

We will see that the outcome is allways even. That's the contradiction.

Do the other one likewise. Assume that the desired result is false (contraposition) and end with a contradiction.