Question

The negation of the compound proposition$p\vee (~p\vee q)$ is

• A. $(p\wedge ~q)\wedge ~p$
• B. $(p\wedge ~q)\vee ~p$
• C. $(p\vee ~q)\vee ~p$
• D. None of these

Answer 1

The correct option is A

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

Find the negation for the given proposition

Given, $p\vee (~p\vee q)$

$\begin{array}{l}~[p\vee (~p\vee q\left)\right]\equiv ~p\wedge ~(~p\vee q)\end{array}$

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

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

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

Hence the correct , option $\left(A\right)$ .