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

$S\wedge \sim r$

$S\wedge (r\wedge\sim S)$

$S\vee (r\vee\sim S)$

$S\wedge r$

Option D

$\sim (\sim S \vee(\sim r\wedge S))$

$\equiv S \wedge (\sim (\sim r\wedge S))$

$\equiv S \wedge (r\vee \sim S))$

$\equiv (S \wedge r)\vee(S\wedge \sim S)$

$\equiv (S \wedge r)\vee F (\because S\wedge\sim S$ is false )

$\equiv S \wedge r$

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