The logical statement $\sim(p \vee q) \vee(\sim p \wedge q)$ is equivalent to
The logical statement $\sim(p \vee q) \vee(\sim p \wedge q)$ is equivalent to
- $\mathrm{q}$
- $\sim q$
- $\sim p$
- p
Solution
$\begin{aligned} & \sim(\mathrm{p} \vee \mathrm{q}) \vee(\sim \mathrm{p} \wedge \mathrm{q}) \equiv(\sim \mathrm{p} \wedge \sim \mathrm{q}) \vee(\sim \mathrm{p} \wedge \mathrm{q}) \text { [De Morgan's law] } \\ & \equiv \sim p \wedge(\sim q \vee q) \quad \text { [Distributive law] } \\ & \equiv \sim p \wedge t \quad[\because \sim q \vee q \equiv t] \\ & \equiv \sim \mathrm{p} \\ & \end{aligned}$
Asked in: MHT CET 2022 (05 Aug Shift 1)
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