Question

If $p$: It is snowing, $q$: I am cold, then the compound statement $"$It is snowing and it is not that I am cold$\text{'}\text{'}$ is given by

• A. $p\wedge \left(~q\right)$
• B. $p\wedge q$
• C. $\left(~p\right)\wedge q$
• D. $\left(~p\right)\wedge \left(~q\right)$
• E. $p\vee \left(~q\right)$

Answer 1

The correct option is A

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

Explanation for correct option :

By the De Morgan's Law, we know that

$\left(~p\right)\mathbf{\vee }\mathbf{(}\mathbf{~}\mathit{q}\mathbf{)}\mathbf{=}\mathbf{~}\left(p\wedge q\right)$

This means if there is a negation of $p$ or negation of $q$ then that will be equal to the negation of $p$ and $q$.

Now, the required statement is that it is snowing and it is not that I am cold.

If it is snowing then there is no negation of $p$. Also, there is ‘and’ as the connector.

The second statement was that I am cold but here it is not that I am cold which means it is a negation of $q$.

From this, we can describe the required statement as $p\wedge ~q$.

Hence, the correct option is (A).