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"

Answer 1

The given compound statement is of the form "if p then q"

$p:xϵZ$ and $x^2$ is even.

q : x is an even integer.

We assume that q is false then x is not an even integer.

$\Rightarrow$ x is an odd integer

$\Rightarrow x^2$ is an odd integer.

$\Rightarrow$ p is false

So when q is false, p is false.

Thus the given compound statement is true.