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(B) To determine if a statement is a tautology,we construct a truth table for each.For statement $(a)$: $(\sim q \wedge (p$ $\rightarrow q))$ $\righta

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$(a)$ and $(b)$ both are tautologies.

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(B) To determine if a statement is a tautology,we construct a truth table for each.For statement $(a)$: $(\sim q \wedge (p$ $\rightarrow q))$ $\rightarrow \sim p$$p, q$$\sim q$$p \rightarrow q$$\sim q \wedge (p \rightarrow q)$$\sim p$$(a)$$T, T$$F$$T$$F$$F$$T$$T, F$$T$$F$$F$$F$$T$$F, T$$F$$T$$F$$T$$T$$F, F$$T$$T$$T$$T$$T$Since all values in the final column are $T$,$(a)$ is a tautology.For statement $(b)$: $((p \vee q) \wedge \sim p) \rightarrow q$$p, q$$p \vee q$$\sim p$$(p \vee q) \wedge \sim p$$(b)$$T, T$$T$$F$$F$$T$$T, F$$T$$F$$F$$T$$F, T$$T$$T$$T$$T$$F, F$$F$$T$$F$$T$Since all values in the final column are $T$,$(b)$ is also a tautology.Therefore,both $(a)$ and $(b)$ are tautologies.

For the statements $p$ and $q$,consider the following compound statements :
$(a)$ $(\sim q \wedge (p$ $\rightarrow q))$ $\rightarrow \sim p$
$(b)$ $((p \vee q) \wedge \sim p) \rightarrow q$
Then which of the following statements is correct?

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For the statements $p$ and $q$,consider the following compound statements :$(a)$ $(\sim q \wedge (p$ $\rightarrow q))$ $\rightarrow \sim p$$(b)$ $((p \vee q) \wedge \sim p) \rightarrow q$Then which of the following statements is correct?