#### Question

Show that the following statement is true by the method of contrapositive.

*p*: *If x is an integer and x*^{2}* is even, then x is also even.*

#### Solution

*p*: If *x* is an integer and *x*^{2} is even, then *x* is also even.

Let *q*: *x* is an integer and *x*^{2} is even.

*r*: *x* is even.

To prove that* p *is true by contrapositive method, we assume that *r* is false, and prove that *q* is also false.

Let *x* is not even.

To prove that *q* is false, it has to be proved that *x* is not an integer or *x*^{2} is not even.

*x* is not even implies that *x*^{2} is also not even.

Therefore, statement *q* is false.

Thus, the given statement *p* is true.

Is there an error in this question or solution?

Solution 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. Concept: Introduction of Validating Statements.