Question

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

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

Answer 1

The correct option is B

$2$ is prime and $3$ is not odd

Explanation for the correct answer:

Let $p$ denote the statement that $2$ is a prime number

Let $q$ denote the statement that $3$ is a odd number

The given statement is that, " If $2$ is a prime number then $3$ is a odd number"

This statement can be written in Boolean format as

$p\to q$

Now to find the negation of this statement

$~\left(p\to q\right)\equiv p\wedge ~q$

Now this Boolean expression is written in word format again as,

$2$ is prime and $3$ is not odd.

Hence, option $\left(B\right)$ is the correct answer.