$\sim (p \vee q) \vee (~ p \wedge q)$ is logically equivalent to

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

The compound statement $(\mathrm{P} \vee \mathrm{Q}) \wedge(\sim \mathrm{P}) \Rightarrow \mathrm{Q}$ is equivalent to:

Consider the following statements :
$P$ : Suman is brilliant
$Q$ : Suman is rich.
$R$ : Suman is honest
the negation of the statement

"Suman is brilliant and dishonest if and only if suman is rich" can be equivalently expressed as

The Boolean expression $ \sim \left( {p \Rightarrow \left( { \sim q} \right)} \right)$ is equivalent to

The converse of the statement $((\sim p) \wedge q) \Rightarrow r$ is