Question

The negation of $\sim s\vee (\sim r\wedge s)$ is equivalent to

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

Answer 1

The correct option is C $s\wedge r$

$\sim (\sim s\vee (\sim r\wedge s\left)\right)=s\wedge (r\vee \sim s)$
$=(s\wedge r)\vee (s\wedge \sim s)$
$=(s\wedge r)\vee f$ (using distributive and complement laws)
$=s\wedge r$