Question

The negation of the proposition "If $2$ is prime then $3$ is odd" is

• A. $2$ is prime and $3$ is not odd
• B. If $2$ is not prime then $3$ is not odd
• C. If $2$ is not prime then $3$ is odd
• D. $2$ is not prime and $3$ is odd.

Answer 1

Answer: (A)

Let p = 2 is prime
q = 3 is odd
p $\to$ q = 2 is prime, then 3 is odd.
Negation of $P \to q$ is $ \sim (p \to q)$
$\Rightarrow \; P \Lambda \sim q$
$\Rightarrow $ 2 is prime and 3 is not odd.