The logical statement $(p \lor q) \land [(\sim p \land q) \lor (p \land \sim q)] \land \sim q$ 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 $x - 17 < 20$.
$S_3: \forall n \in N, x^2 + 3x - 10 = 0$.
$S_4: \forall n \in N, n^2 \geq 1$.

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.....

Write the negation of the following statement:
$r:$ For every real number $x$,either $x > 1$ or $x < 1.$

$(p \wedge \sim q \wedge \sim r) \vee (\sim p \wedge q \wedge \sim r) \vee (\sim p \wedge \sim q \wedge r)$ is equivalent to-

The contrapositive of the statement: "If the weather is fine then my friends will come and we go for a picnic." is