Q12 (c)

Contrapositive:

If $a$ is not odd then $a^2-2a+7$ is not even.

This is equivalent to:

If $a$ is even then $a^2-2a+7$ is odd.

Let $a=2k$ where $k$ is an integer.

Then:

$$a^2-2a+7=(2k)^2-2(2k)+7$$ $$=2(2k^2-2k+3)+1$$

$2k^2-2k+3$ is an integer as $k$ is an integer.

Therefore, $2(2k^2-2k+3)+1$ is odd.

Thus, if $a$ is even then $a^2-2a+7$ is odd.

Thus, if $a^2-2a+7$ is even then $a$ is odd.