Question

Assertion :The contrapositive and converse of the statement: "If $x$ is a prime number, then $x$ is odd" are:
Contrapositive: "If $x$ is not odd, then $x$ is not a prime number.
Converse: If $x$ is odd, then $x$ is a prime number. Reason: If statement $p$ implies $q$, then its contrapositive is $\sim q$ implies $\sim p$, and its converse is $q$ implies $p$.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
• C. Assertion is correct but Reason is incorrect.
• D. Both Assertion and Reason are incorrect.

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.

Contrapositive is the inverse of converse of a statement. Converse of a statement "p implies q" will be "q implies p* i.e; the hypothesis and conclusion are interchanged. Contrastive is the inverse of "q implies p" or "~q implies ~p". It is obtained by adding "not" to both hypothesis and conclusion of the converse statement.

Hence both assertion and reason are correct.