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

If the Boolean expression $( p \Rightarrow q ) \Leftrightarrow( q *(\sim p ))$ is a tautology, then the Boolean expression $p *(\sim q )$ is equivalent to

If $P$ and $Q$ are two statements, then which of the following compound statement is a tautology?

Negation of the compound proposition : If the examination is difficult, then I shall pass if I study hard

The conditional $(p \wedge q)  \Rightarrow  p$ is :-

The statement $[(p \wedge  q) \rightarrow p] \rightarrow (q \wedge  \sim q)$ is