Among the statements

$(S1)$: $(p \Rightarrow q) \vee((\sim p) \wedge q)$ is a tautology

$(S2)$: $(q \Rightarrow p) \Rightarrow((\sim p) \wedge q)$ is a contradiction

Which of the following Boolean expressions is not a tautology ?

The proposition $ \sim \left( {p\,\vee \sim q} \right) \vee  \sim \left( {p\, \vee q} \right)$ is logically equivalent to

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

Let $\Delta, \nabla \in\{\wedge, \vee\}$ be such that $( p \rightarrow q ) \Delta( p \nabla q )$ is a tautology. Then

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