Question

The negation of the Boolean expression $p\vee (~p\wedge q)$ is equivalent to:

• A. $p\wedge ~q$
• B. $~p~q$
• C. $~pq$
• D. $~p\wedge ~q$

Answer 1

The correct option is D

$~p\wedge ~q$

Find negation of the given Boolean expression

Given, $p\vee (~p\wedge q)$ can be simplified as,

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

$=\left(T\right)\wedge \left(p\vee q\right)$

$=\left(p\vee q\right)$

Now negation of $\left(p\vee q\right)$ is

$~(p\vee q)=~p\wedge ~q$

so the negation of $p\vee (~p\wedge q)$ is $~p\wedge ~q$,

Hence the correct option $\left(D\right)$.