Which one of the following is a tautology ?
$\mathrm{P} \wedge(\mathrm{P} \vee \mathrm{Q})$
$\mathrm{P} \vee(\mathrm{P} \wedge \mathrm{Q})$
$\mathrm{Q} \rightarrow(\mathrm{P} \wedge(\mathrm{P} \rightarrow \mathrm{Q}))$
$(\mathrm{P} \wedge(\mathrm{P} \rightarrow \mathrm{Q})) \rightarrow \mathrm{Q}$
The statement $[(p \wedge q) \rightarrow p] \rightarrow (q \wedge \sim q)$ is
The Boolean expression $\left( {\left( {p \wedge q} \right) \vee \left( {p \vee \sim q} \right)} \right) \wedge \left( { \sim p \wedge \sim q} \right)$ is equivalent to
Let $p , q , r$ be three logical statements. Consider the compound statements $S _{1}:((\sim p ) \vee q ) \vee((\sim p ) \vee r ) \text { and }$ and $S _{2}: p \rightarrow( q \vee r )$ Then, which of the following is NOT true$?$
The compound statement $(\sim( P \wedge Q )) \vee((\sim P ) \wedge Q ) \Rightarrow((\sim P ) \wedge(\sim Q ))$ is equivalent to
The proposition $ \sim \left( {p\,\vee \sim q} \right) \vee \sim \left( {p\, \vee q} \right)$ is logically equivalent to