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

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?

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

If $p \to ( \sim p\,\, \vee \, \sim q)$ is false, then the truth values of  $p$ and  $q$ are respectively .

$(p\; \wedge \sim q) \wedge (\sim p \wedge q)$ is

The propositions $(p \Rightarrow \;\sim p) \wedge (\sim p \Rightarrow p)$ is a