The logical statement [sim(sim p vee q) vee ( | vedclass

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(A) Given expression: $[\sim(\sim p \vee q) \vee (p \wedge r)] \wedge (\sim q \wedge r)$ Applying De Morgan's law: $[(p \wedge \sim q) \vee (p \wedge

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$(p \wedge r) \wedge \sim q$

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(A) Given expression: $[\sim(\sim p \vee q) \vee (p \wedge r)] \wedge (\sim q \wedge r)$ Applying De Morgan's law: $[(p \wedge \sim q) \vee (p \wedge r)] \wedge (\sim q \wedge r)$ Applying Distributive law: $[p \wedge (\sim q \vee r)] \wedge (\sim q \wedge r)$ Applying Associative law: $p \wedge [(\sim q \vee r) \wedge (\sim q \wedge r)]$ Since $(\sim q \vee r) \wedge (\sim q \wedge r) = (\sim q \wedge r)$,the expression becomes: $p \wedge (\sim q \wedge r)$ Rearranging using Commutative law: $(p \wedge r) \wedge \sim q$

The logical statement $[\sim(\sim p \vee q) \vee (p \wedge r)] \wedge (\sim q \wedge r)$ is equivalent to

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