The logical statement $(\sim(\sim \mathrm{p} \vee \mathrm{q}) \vee(\mathrm{p} \wedge \mathrm{r})) \wedge(\sim \mathrm{q} \wedge \mathrm{r})$ is equivalent to

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Aicharya · Accepted Answer

$\begin{aligned} & {[\sim(\sim p \vee q) \vee(p \wedge r)] \wedge(\sim q \wedge r)} \ & \equiv[(p \wedge \sim q) \vee(p \wedge r)] \wedge(\sim q \wedge r) & \Rightarrow \ldots[	ext { De Morgan's law }] \end{aligned}$ $\equiv \mathrm{p} \wedge(\sim \mathrm{q} \vee \mathrm{r}) \wedge(\sim \mathrm{q} \wedge \mathrm{r}) \quad \ldots[$ Distributive law $]$ $\equiv p \wedge[(\sim q \vee r) \wedge \sim q] \wedge r^{\prime} .. [	ext { Associative law] }$ $\equiv \mathrm{p} \wedge(\sim \mathrm{q}) \wedge\mathrm{r} \quad \ldots[$ Absórption law] $\equiv(p \wedge r) \wedge \sim q$ .. [Commutative and Associative law]

The logical statement $(\sim(\sim \mathrm{p} \vee \mathrm{q}) \vee(\mathrm{p} \wedge \mathrm{r}))…

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