Question

The negation of the statement $~p\wedge (p\vee q)$ is∶

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

Answer 1

The correct option is D

$p\vee ~q$

Find the negation of the given statement

Negation of $~p\wedge (p\vee q)$ is given as,

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

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

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

$\equiv T\wedge (p\vee ~q)$ where, $T$ is tautology

$\equiv p\vee ~q$

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

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