The statement 'If $x$ is a prime number, then $x$ is odd' is false. Which of the following is a counterexample?

Solution

1. The statement is $p⟹q$ where $p$ is '$x$ is prime' and $q$ is '$x$ is odd'.
2. A counterexample must make $p$ true and $q$ false.
3. For $x=2$, $x$ is prime (true) and $x$ is odd (false).
4. Thus, $x=2$ is a counterexample to the statement.
5. Hence the answer is (B).