The logical expression $[p \wedge (q \vee r)] \vee [(\sim p \wedge q) \vee (\sim p \wedge r)]$ is equivalent to

Given $p$: $A$ man is a judge,$q$: $A$ man is honest. If $S_1$: If a man is a judge,then he is honest; $S_2$: If a man is a judge,then he is not honest; $S_3$: $A$ man is not a judge or he is honest; $S_4$: $A$ man is a judge and he is honest. Then:

The statement pattern $(p \lor q) \to \sim r$ is logically equivalent to

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

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

The Boolean expression $(p \wedge \sim q) \vee q \vee (\sim p \wedge q)$ is equivalent to: