Question

Using contrapositive method prove that if $n^2$ is an even integer, then n is also an even integer.

Answer 1

Let p: $n^2$ is an even integer, then n is also an even integer.

q: n is even integer.

$\therefore$ ~ p : $n^2$ is not an even integer.

$\therefore$ ~ q : n is not an even integer.

Since contrapositive of $p\to q$ is given by ~ q $\to$ ~ p

Hence contrapositive of given statement is :

If n is not an even integer, then $n^2$ is not an even integer.

Here if ~ q is true then ~ p is also true.

$\therefore$ If $n^2$ is an even integer, then 'n' is also an even integer.

Hence proved.