Which of the following is the contrapositive of the statement 'If $x$ is a prime number, then $x$ is odd'?

Solution

1. Identify the original statement as an implication of the form $p⟹q$, where $p$ is '$x$ is a prime number' and $q$ is '$x$ is odd'.
2. Recall that the contrapositive of $p⟹q$ is defined as $\neg q⟹\neg p$.
3. Negate the conclusion $q$ to get 'x is not odd' and negate the hypothesis $p$ to get 'x is not a prime number'.
4. Form the contrapositive statement by placing the negated conclusion first: 'If $x$ is not odd, then $x$ is not a prime number'.
5. Hence the answer is (A).