The proposition $p \Rightarrow \sim (p \wedge \sim q)$ is

The contrapositive of the statement "$I$ go to school if it does not rain" is

The logical statement $(p$ $\Rightarrow q) \wedge (q$ $\Rightarrow \sim p)$ is equivalent to

The maximum number of compound propositions,out of $p \vee r \vee s$,$p \vee \sim r \vee \sim s$,$p \vee \sim q \vee s$,$\sim p \vee \sim r \vee s$,$\sim p \vee \sim r \vee \sim s$,$\sim p \vee q \vee \sim s$,$q \vee r \vee \sim s$,$q \vee \sim r \vee \sim s$,$\sim p \vee \sim q \vee \sim s$ that can be made simultaneously true by an assignment of the truth values to $p, q, r$ and $s$,is equal to

Let $p$: $A$ man is a judge.
$q$: He is honest.
The inverse of $p \rightarrow q$ is

The negation of the statement $p \rightarrow (q \wedge r)$ is equal to .........