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

The negation of $(p \wedge q) \rightarrow ((p \vee r) \rightarrow\, \sim q)$ is equivalent to ...

The statement pattern $[(p \wedge q) \rightarrow (\sim p \vee r)] \vee [(\sim p \vee r) \rightarrow (p \wedge q)]$ is

In $\triangle ABC$, with usual notation, if cot A, cot B, cot C are in arithmetic progression, then