Question

If $p:7$is not greater than 4 and $q:$Paris is in France, are two statements. Then, $~(p\vee q)$ is the statement :

• A. $7$ is greater than $4$ or Paris is not in France
• B. $7$ is not greater than $4$ and Paris is not in France
• C. $7$ is greater than $4$ and Paris is in France
• D. $7$is not greater than $4$ or Paris is not in France
• E. $7$ is greater than $4$ and Paris is not in France

Answer 1

The correct option is B

$7$ is not greater than $4$ and Paris is not in France

Explanation for the correct option.

Given $p:7$is not greater than $4.$

We know that, $~(p\vee q)=~p\wedge ~q$

Clearly, the above statement is false as $7$ is always greater than $4.$

$q:$Paris is in France.

Then, $~q$ means Paris is not in France.

$p:$ $7$ is not greater than $4$

Then, $~p$ Paris is not in France.

Therefore,$~(p\vee q)$ means $7$ is not greater than $4$ and Paris is not in France.

Hence, option B is correct.