Which of the following statements is correct? | vedclass

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(B) We analyze each statement:$S_1: \sim(p \rightarrow \sim q) \equiv p \wedge \sim(\sim q) \equiv p \wedge q$. Thus,$S_1$ is a tautology (correct).$S

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Statement $S_1$ is correct

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(B) We analyze each statement:$S_1: \sim(p \rightarrow \sim q) \equiv p \wedge \sim(\sim q) \equiv p \wedge q$. Thus,$S_1$ is a tautology (correct).$S_2: (p \wedge q) \wedge (\sim p \vee \sim q) \equiv (p \wedge q) \wedge \sim(p \wedge q)$,which is a contradiction,not a tautology.$S_3: [p \wedge (p$ $\rightarrow \sim q)]$ $\rightarrow q \equiv [p \wedge (\sim p \vee \sim q)]$ $\rightarrow q \equiv [(p \wedge \sim p) \vee (p \wedge \sim q)]$ $\rightarrow q \equiv (F \vee (p \wedge \sim q))$ $\rightarrow q \equiv (p \wedge \sim q)$ $\rightarrow q \equiv \sim(p \wedge \sim q) \vee q \equiv (\sim p \vee q) \vee q \equiv \sim p \vee q$. This is a contingency,not a contradiction.$S_4: p$ $\rightarrow (q$ $\rightarrow p) \equiv \sim p \vee (\sim q \vee p) \equiv (\sim p \vee p) \vee \sim q \equiv T \vee \sim q \equiv T$. This is a tautology,not a contingency.Therefore,only $S_1$ is correct.

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