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:

The negation of the converse of the statement $p \lor q$ is:

The statement $\sim[p \vee (\sim(p \wedge q))]$ is equivalent to

The negation of $p \rightarrow (\sim p \vee q)$ is

Which of the following statements is/are False?
$S_1: \exists n \in N$, such that $n^2 + n + 2$ is divisible by $4$.
$S_2: \exists x \in N$, such that $x - 17 < 20$.
$S_3: \forall n \in N, x^2 + 3x - 10 = 0$.
$S_4: \forall n \in N, n^2 \geq 1$.

Let $p$ be the statement '$x$ is an irrational number',$q$ be the statement '$y$ is a transcendental number',and $r$ be the statement '$x$ is a rational number or $y$ is a transcendental number'.
Statement-$1$: $r$ is equivalent to $q \lor p$.
Statement-$2$: $r$ is equivalent to $(p \Leftrightarrow \sim q)$.