The statement pattern $(p \lor q) \to \sim r$ 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 $x - 17 < 20$.
$S_3 : \forall n \in N, n^2 + 3n - 10 = 0$.
$S_4 : \forall n \in N, n^2 \ge 1$.

The symbolic form of the statement "If it does not rain today or $I$ will not go to school,then $I$ will meet my friend and $I$ will go to watch a movie" is:
$p$: It rains today
$q$: $I$ am going to school
$r$: $I$ will meet my friend
$s$: $I$ will go to watch a movie

Determine which of the following is not a statement.

If the statements $p, q$ and $r$ have the truth values $F, T, F$ respectively,then the truth values of the statement patterns $(p \wedge \sim q) \rightarrow r$ and $(p \vee q) \rightarrow r$ are respectively

Write the negation of the following statement:
$\sqrt{2}$ is not a complex number.