Among the statements:

$(S1)$ $\quad(( p \vee q ) \Rightarrow r ) \Leftrightarrow( p \Rightarrow r )$

$(S2) \quad(( p \vee q ) \Rightarrow r ) \Leftrightarrow(( p \Rightarrow r ) \vee( q \Rightarrow r ))$

If the inverse of the conditional statement $p \to \left( { \sim q\ \wedge  \sim r} \right)$ is false, then the respective truth values of the statements $p, q$ and $r$ is

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

The expression $ \sim ( \sim p\, \to \,q)$ is logically equivalent to

Negation of the statement $P$ : For every real number, either $x > 5$ or $x < 5$ is