Chapter 1 - Section 1.7 - Introduction to Proofs - Exercises - Page 91: 3

Here is the proof of this statement. We are to prove that square of the even number is also even.

SOLUTION: Let, Even number (a) = 2k Now, $a^2$ = $(2k)^2$ = $4k^2$ = 2$(2k^2)$ = even. REASON: As, k is any integer and $2k^2$ is multiple of 2. Hence, Proved.