Show that the following statement is true by the method of contrapositive. p: If x is an integer and x² is even, then x is also even.

p: if x is an integer and x² is even, then x is also even.

Let p: if x is an integer and x² is even

q: x is even

The given statement is if p then q

Method of Contrapositive

By assuming q is not true & prove that p must be true

i.e. ~q ⇒ ~p

Let q is not true & prove p is also not true.

⇒ q is not true

i.e. x is not even

i.e. x is odd

i.e. x = 2n + 1

Squaring both side

(x)² = (2n + 1)²

⇒ x² = 4n² + 4n + 1

⇒ x² = 4(n² + n) + 1

⇒ x² is odd

⇒ p is also not true

Hence the given statement is true.