Question

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.

Answer 1

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

Let q: x is an integer and x² 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 x² is not even.

x is not even implies that x² is also not even.

Therefore, statement q is false.

Thus, the given statement p is true.