Which of the following is a tautology ?
Correct Option: 1
Option (1) is
$\sim \mathrm{p} \wedge(\mathrm{p} \vee \mathrm{q}) \rightarrow \mathrm{q}$
$\equiv(\sim \mathrm{p} \wedge \mathrm{p}) \vee(\sim \mathrm{p} \wedge \mathrm{q}) \rightarrow \mathrm{q}$
$\equiv \mathrm{C} \vee(\sim \mathrm{p} \wedge \mathrm{q}) \rightarrow \mathrm{q}$
$\equiv(\sim \mathrm{p} \wedge \mathrm{q}) \rightarrow \mathrm{q}$
$\equiv \sim(\sim \mathrm{p} \wedge \mathrm{q}) \vee \mathrm{q}$
$\equiv(p \vee \sim q) \vee q$
$\equiv(p \vee q) \vee(\sim q \vee q)$
$\equiv(p \vee q) \vee t$
so $\sim \mathrm{p} \wedge(\mathrm{p} \vee \mathrm{q}) \rightarrow \mathrm{q}$ is a tautology
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