Which of the following statements is a tautology?

Question:
Which of the following statements is a tautology?

$\sim(\mathrm{p} \vee \sim \mathrm{q}) \rightarrow \mathrm{p} \vee \mathrm{q}$
$\sim(\mathrm{p} \wedge \sim \mathrm{q}) \rightarrow \mathrm{p} \vee \mathrm{q}$
$\sim(\mathrm{p} \vee \sim \mathrm{q}) \rightarrow \mathrm{p} \wedge \mathrm{q}$
$\mathrm{p} \vee(\sim \mathrm{q}) \rightarrow \mathrm{p} \wedge \mathrm{q}$

Correct Option: 1

Solution:

$\sim(\mathrm{p} \vee \sim \mathrm{q}) \rightarrow \mathrm{p} \vee \mathrm{q}$

$(\sim \mathrm{p} \wedge \mathrm{q}) \rightarrow \mathrm{p} \vee \mathrm{q}$

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

$\sim(\sim \mathrm{p} \wedge f)$

(1) Option

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