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

The negation of the Boolean expression $\sim s \vee (\sim r \wedge s)$ is equivalent to

$(p \wedge \sim q) \wedge (\sim p \wedge q)$ is

If the Boolean expression $(p \Rightarrow q) \Leftrightarrow (q * (\sim p))$ is a tautology,then the Boolean expression $p * (\sim q)$ is 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 $x - 17 < 20$.
$S_3: \forall n \in N, x^2 + 3x - 10 = 0$.
$S_4: \forall n \in N, n^2 \ge 1$.

The logical expression $[p \wedge (q \vee r)] \vee [(\sim p \wedge q) \vee (\sim p \wedge r)]$ is equivalent to