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

Let $p$ and $q$ be two statements.Then $\sim( p \wedge( p \Rightarrow \sim q ))$ is equivalent to

The statement $p \to ( q \to p)$ is equivalent to

Negation of $p \wedge (\sim q \vee \sim r)$ is -

The contrapositive of statement 'If Jaipur is capital of Rajasthan, then Jaipur is in India' is 

The statement $B \Rightarrow((\sim A ) \vee B )$ is equivalent to