Question

If $S(p,q,r)=(~p)\vee [~(q\wedge r\left)\right]$ is a compound statement, then $S(~p,~q,~r)$ is

• A. $~S(p,q,r)$
• B. $S(p,q,r)$
• C. $p\vee (q\wedge r)$
• D. $p\wedge (q\vee r)$
• E. $S(p,q,~r)$

Answer 1

The correct option is D

$p\wedge (q\vee r)$

Explanation for the correct option.

Given, $S(p,q,r)=(~p)\vee [~(q\wedge r\left)\right]$.

$\begin{array}{rcl}S(~p,~q,~r)& =& ~\left(~p\right)\vee [~\left(~q\wedge ~r\right)]\\ & =& p\vee [~(~q)\vee ~(~r\left)\right]\\ & =& p\vee (q\vee r)\end{array}$

Hence, option C is correct.