The statement $p$ $\Rightarrow (q$ $\Rightarrow p)$ is logically equivalent to .....

Which of the following is logically equivalent to $(p \wedge q)$?

If $ab = 0$,write the contrapositive of the statement $(a = 0 \text{ or } b = 0)$.

The logical statement $(p \lor q) \land [(\sim p \land q) \lor (p \land \sim q)] \land \sim q$ is logically equivalent to ...

The simplest form of the following switching circuit 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 $x - 17 < 20$.
$S_3 : \forall n \in N, n^2 + 3n - 10 = 0$.
$S_4 : \forall n \in N, n^2 \ge 1$.