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The negation of the statement pattern $\sim \mathrm{S} \vee(\sim \mathrm{r} \wedge \mathrm{s})$ is equivalent to
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The correct answer is:
$\mathrm{s} \wedge \mathrm{r}$
$\begin{aligned}
& \sim(\sim s \vee(\sim r \wedge s)) \\
& \equiv s \wedge \sim(\sim r \wedge s)...[De Morgan's law] \\
& \equiv s \wedge(r \vee \sim s)......[De Morgan's law] \\
& \equiv(s \wedge r) \vee(s \wedge \sim s)...[Distributive law] \\
& \equiv(s \wedge r) \vee F...[Complement law] \\
& \equiv s \wedge r...[Identity law]
\end{aligned}$
& \sim(\sim s \vee(\sim r \wedge s)) \\
& \equiv s \wedge \sim(\sim r \wedge s)...[De Morgan's law] \\
& \equiv s \wedge(r \vee \sim s)......[De Morgan's law] \\
& \equiv(s \wedge r) \vee(s \wedge \sim s)...[Distributive law] \\
& \equiv(s \wedge r) \vee F...[Complement law] \\
& \equiv s \wedge r...[Identity law]
\end{aligned}$
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