The proposition $p \rightarrow \sim( p \wedge \sim q )$ is equivalent to

Find the component statements of the following and check whether they are true or not.
All prime numbers are either even or odd.

Let $a: \sim(p \wedge \sim r) \vee(\sim q \vee s)$ and $b: (p \vee s) \leftrightarrow(q \wedge r)$. If the truth values of $p$ and $q$ are $T$ and that of $r$ and $s$ are $F$,then the truth values of $a$ and $b$ are respectively...

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

Let $\Delta, \nabla \in \{\wedge, \vee\}$ be such that $( p \rightarrow q ) \Delta ( p \nabla q )$ is a tautology. Then

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