Question

The contrapositive of the converse of the statement ''If $x$ is a prime number then $x$ is odd'' is

• A. If $x$ is not a prime number then $x$ is odd.
• B. If $x$ is not an odd number then $x$ is not a prime number.
• C. If $x$ is a prime number then it is not odd.
• D. If $x$ is not a prime number then $x$ is not an odd.

Answer 1

The correct option is D If $x$ is not a prime number then $x$ is not an odd.

Let the statements be:
$p:x$ is a prime number.
$q:x$ is odd.
Then, the given statement is $p\Rightarrow q$
Converse of $p\Rightarrow q$ is $q\Rightarrow p$
Contrapositive of converse of $p\Rightarrow q$ is $\sim p\Rightarrow \sim q$
Thus, the contrapositive of the converse of the given statement is ''If $x$ is not a prime number then $x$ is not an odd.''