Show that the square of an even number is an even number, using the direct proof.

proved

Explanation:

Suppose n is an even number and therefore n = 2k for some integer k

now n^2 = (2k) ^2 = 4k^2

= 2*2k^2

= again 2k^2 would be an integer hence, two times an integer is an even number

Therefore, we can conclude that n^2 is an even integer.