Letabe an integer. Prove by contraposition that ifa^{2}- 11a+ 22 is odd thenais even.

Fill in the gaps in the following proof.

Supposeais odd, soa= 2n+ 1 for some integern.

Then in terms ofn,a^{2}- 11a+ 22 = 2(..........)

soa^{2}- 11a+ 22 is an(.........)

Hence, by contraposition, ifa^{2}- 11a+ 22 is odd thenais even.