Show that he following statement is true by the method of contrapositive: `p\ : If\ x` is an integer `x^2` is even then `x` is also even.

Explanation

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.

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