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

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

Which of the following statement$(s)$ is/are not true?
$I$) If $1$ is not a prime number, then $2$ is not a prime number.
$II$) $e$ is a vowel and $12 \times 3 = 36$.
$III$) It is not true that $14$ is a composite number and $3$ is an even number.
$IV$) $\sqrt{5}$ is an irrational number, but $3 + \sqrt{5}$ is a complex number.

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

Let $p$ and $q$ be two statements. Amongst the following,the statement that is equivalent to $p \to q$ is

If the inverse of the conditional statement $p \to (\sim q \wedge \sim r)$ is false,then the respective truth values of the statements $p, q,$ and $r$ are: