Question

For any two statements $p$ and $q$, $~(p\vee q)\vee (~p\wedge q)$ is logically equivalent to

• A. $p$
• B. $~p$
• C. $q$
• D. $~q$

Answer 1

The correct option is B

$~p$

Explanation for the correct option:

Given that $~(p\vee q)\vee (~p\wedge q)$

$$\begin{gathered} =(~p\wedge ~q)\vee (~p\wedge q) \\ =~p\wedge (~q\vee q) \\ =~p\wedge T \\ =\mathbf{~}\mathbf{}\mathit{p} \end{gathered}$$

Hence, Option ‘B’ is Correct.