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

The Statement that is $TRUE$ among the following is

Among the two statements

$(S1):$ $( p \Rightarrow q ) \wedge( q \wedge(\sim q ))$ is a contradiction and

$( S 2):( p \wedge q ) \vee((\sim p ) \wedge q ) \vee$

$( p \wedge(\sim q )) \vee((\sim p ) \wedge(\sim q ))$ is a tautology

The Boolean expression $\sim\left( {p\; \vee q} \right) \vee \left( {\sim p \wedge q} \right)$ is equivalent ot :

The Boolean expression $(\mathrm{p} \wedge \mathrm{q}) \Rightarrow((\mathrm{r} \wedge \mathrm{q}) \wedge \mathrm{p})$ is equivalent to :

For the statements $p$ and $q$, consider the following compound statements :

$(a)$ $(\sim q \wedge( p \rightarrow q )) \rightarrow \sim p$

$(b)$ $((p \vee q) \wedge \sim p) \rightarrow q$

Then which of the following statements is correct?