Question

The negation of $\sim sv(\sim rs)$ is equivalent to

• A. $s\wedge \sim r$
• B. $s\wedge (r\wedge \sim s)$
• C. $s\vee \left(s\wedge \sim r\right)$
• D. $s\wedge r$

Answer 1

The correct option is C $s\vee \left(s\wedge \sim r\right)$

$\begin{array}{c}Wehave\\ \sim s\wedge \left(\sim s\wedge r\right)\\ =\sim \left[\sim s\wedge \left(\sim s\wedge r\right)\right]\\ =\sim \left(\sim s\right)\wedge \sim \left(\sim s\wedge r\right)\\ =s\wedge \left(s\vee \sim r\right)\\ =\left(s\wedge s\right)\vee \left(s\wedge \sim r\right)\\ =s\vee \left(s\wedge \sim r\right)\\ Hence,theoptionCisthecorrectanswer.\end{array}$