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:
$(\sim p \wedge q) \rightarrow(p \vee q)$
$\Rightarrow \sim\{(\sim p \wedge q) \wedge(\sim p \wedge \sim q)\}$
$\Rightarrow \sim\{p \wedge f\}$
