If $p \Rightarrow (\sim p \vee q)$ is false, the truth values of $p$ and $q$ are respectively

The negation of the Boolean expression $ \sim \,s\, \vee \,\left( { \sim \,r\, \wedge \,s} \right)$ is equivalent to

The compound statement $(\sim( P \wedge Q )) \vee((\sim P ) \wedge Q ) \Rightarrow((\sim P ) \wedge(\sim Q ))$ is equivalent to

Let $*, \square \in\{\wedge, \vee\}$ be such that the Boolean expression $(\mathrm{p} * \sim \mathrm{q}) \Rightarrow(\mathrm{p} \square \mathrm{q})$ is a tautology. Then :

The false statement in the following is

The logical statement $[ \sim \,( \sim \,P\, \vee \,q)\, \vee \,\left( {p\, \wedge \,r} \right)\, \wedge \,( \sim \,q\, \wedge \,r)]$ is equivalent to