Which of the following statements is a tautology?

Question:
Which of the following statements is a tautology?

(1) $p \vee(\sim q) \rightarrow p \wedge q$
(2) $\sim(p \wedge \sim \mathrm{q}) \rightarrow p \vee q$
(3) $\sim(p \vee \sim q) \rightarrow P \wedge q$
(4) $\sim(P \vee \sim q) \rightarrow p \vee q$

Correct Option: , 4

Solution:

$(\sim p \wedge q) \rightarrow(p \vee q)$

$\Rightarrow \sim\{(\sim p \wedge q) \wedge(\sim p \wedge \sim q)\}$

$\Rightarrow \sim\{p \wedge f\}$

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