The correct logical equivalence from the following is /are ___
(I) $p \to (q \to r) \equiv (p \wedge q) \to r$
(II) $(p \to q) \to r \equiv p \to (q \vee r)$
(III) $(p \to q) \to r \equiv (p \to r) \wedge (\sim q \to r)$
(IV) $p \to (q \to r) \equiv q \to (p \to r)$

The contrapositive of the statement pattern $[p \vee (p \to q)] \to (p \wedge \sim q)$ is

The negation of the converse of $p \vee q$ 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 $x - 17 < 20$.
$S_3 : \forall\, n \in N, \quad x^2 + 3x - 10 = 0$.
$S_4 : \forall\, n \in N, \quad n^2 \geq 1$.