Question

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

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

Answer 1

The correct option is B $s\wedge r$

Given,
$\Rightarrow \sim (\sim s\vee (\sim r\wedge s\left)\right)$
$\Rightarrow s\wedge (r\vee \sim s)$
$\Rightarrow (s\wedge r)\vee (s\wedge \sim s)$
$\Rightarrow (s\wedge r)\wedge \left(s\right)$
$\Rightarrow (s\wedge r)$