Consider the following statements :

$A$ : Rishi is a judge.

$B$ : Rishi is honest.

$C$ : Rishi is not arrogant.

The negation of the statement "if Rishi is a judge and he is not arrogant, then he is honest" is

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

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

The negative of the statement $\sim p \wedge(p \vee q)$ is

If $P \Rightarrow \left( {q \vee r} \right)$ is false, then the truth values of $p, q, r$ are respectively

The negation of $ \sim s \vee \left( { \sim r \wedge s} \right)$ is equivalent to