The negation of the inverse of the statement $\sim p \lor q$ is...

If $p$: The total prime numbers between $2$ to $100$ are $26$.
$q$: Zero is a complex number.
$r$: Least common multiple ($L$.$C$.$M$.) of $6$ and $7$ is $6$.
Then which of the following is correct?

The conditional statement $(p \wedge q) \implies p$ is:

Consider the statement patterns:
$A. (q \to p) \lor (p \to q)$
$B. (\sim p \lor \sim q) \leftrightarrow \sim (p \land q)$
$C. [(p \lor q) \land \sim p] \land \sim q$
$D. (p \land q) \land (\sim p \lor \sim q)$
Which of the following is true regarding these statement patterns?

If $p$ and $q$ are simple propositions,then $p \Rightarrow q$ is false when

$\sim (p \Rightarrow q) \Leftrightarrow \sim p \vee \sim q$ is