Question

The negation of the statement: 'He is rich and happy' is given by

• A. he is not rich and not happy
• B. he is not rich or not happy
• C. he is rich and happy
• D. he is not rich and happy

Answer 1

The correct option is B

he is not rich or not happy

Explanation for the correct answer:

Let $p$ denote the statement that ‘He is rich’

Let $q$ denote the statement that ‘ He is happy’

The given statement is that, 'He is rich and happy'

This statement can be written in Boolean format as $p\wedge q$

The negation of this statement can be written as

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

Now this Boolean expression is written in word format again as

$\Rightarrow$ 'He is not rich or not happy.'

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