The proposition $\sim (p \vee \sim q) \vee \sim (p \vee q)$ is logically equivalent to

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 $x - 17 < 20$.
$S_3: \forall n \in N, x^2 + 3x - 10 = 0$.
$S_4: \forall n \in N, n^2 \ge 1$.

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.

Write the following statement in the form of "if-then":
The banana trees will bloom if it stays warm for a month.

$p \Rightarrow q$ can also be written as

If $\sim p \lor q$ is false, then which of the following is correct?