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

Let $p, q, r$ be three statements such that the truth value of $(p \wedge q) \rightarrow (\sim q \vee r)$ is $F$. Then the truth values of $p, q, r$ are respectively:

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 statements $p, q$ and $r$ have truth values $T, F$ and $F$ respectively. The truth values of a logical statement $[\sim (p \wedge \sim q) \vee (q \vee \sim r)]$ and its dual are, respectively.....

If $q$ is false and $p \wedge q \leftrightarrow r$ is true,then which of the following is a tautology?

The negation of the statement "For all real numbers $x$ and $y, x+y=y+x$" is