If $\left( {p \wedge  \sim q} \right) \wedge \left( {p \wedge r} \right) \to  \sim p \vee q$ is false, then the truth values of $p, q$ and $r$ are respectively

The proposition $\left( { \sim p} \right) \vee \left( {p\, \wedge  \sim q} \right)$

Among the statements:

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

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

Statement $\quad(P \Rightarrow Q) \wedge(R \Rightarrow Q)$ is logically equivalent to

The statement $p → (p \leftrightarrow  q)$ is logically equivalent to :-

Negation of “Paris in France and London is in England” is