The statement pattern $p \wedge (q \vee \sim p)$ is equivalent to

If the truth value of the compound statement $[(p \lor q) \land (q \to r) \land (\sim r)] \to (p \land q)$ is $False$, then the truth values of $p \to q$ and $q \to p$ are respectively...

Negation of the statement "The payment will be made if and only if the work is finished in time." 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 $x - 17 < 20$.
$S_3 : \forall n \in N, n^2 + 3n - 10 = 0$.
$S_4 : \forall n \in N, n^2 \ge 1$.

Rewrite the following statement in the form "$p$ if and only if $q$":
For you to get an $A$ grade,it is necessary and sufficient that you do all the homework regularly.

Which of the following statements is logically equivalent to $\sim (p \leftrightarrow q)$?