Question

Prove: For all integers n, if n2 is odd, then n is odd. Use a proof by contraposition, as in Lemma 1.1.

Answer 1

The contrapositive of above is "If n is not odd then n^2 is not odd" or "If n is even then n^2 is even".

So, let assume that n is even
$n=2k, k\in \mathbb{Z}$
then
$n^2=(2k)^2=4k^2$
which is even q.e.d.