Answer
See below.
Work Step by Step
(a) To prove the statement by contraposition, we need to prove "for any integer $n$, if $n$ is not odd, then $n^2$ will not be odd". To prove, let $n=2k$ be an even number, we have $n^2=4k^2$ which is an even number (not odd). Thus we proved the statement by contraposition.
(b) To prove the statement by contradiction, suppose there exist an integer $n$, such that $n^2$ is odd while $n$ is even". Let $n=2k$, we have
$n^2=4k^2$, an even number which contradicts to the condition that $n^2$ is odd. Thus, we proved the statement by contradiction.
