Question

Write the converse of contrapositive of the statement "if $n$ is an even number, then square of $n$ is also an even number. "

• A. If $n$ is an even number,then square of $n$ is not an even number.
• B. If $n$ is not an even number,then square of $n$ is also not an even number.
• C. If $n$ is not an even number,then square of $n$ is an even number.
• D. If square of $n$ is not an even number then $n$ is not an even number.

Answer 1

The correct option is D If square of $n$ is not an even number then $n$ is not an even number.

For any conditional staements $p\to q$
Converse statement is $q\to p$
Inverse statement is $\sim p\to \sim q$
Contrapositive statement is $\sim q\to \sim p$
Performing any two action always result in third one.
So, in this case
$p$= $n$ is a even number
$q$= square of $n$ is also a even number.
Converse of contrapositive statement is inverse statement $\sim p\to \sim q$
$\Rightarrow$ If $n$ is not an even number,then square of $n$ is also not an even number.