The contrapositive of $\sim q \to p$ is equivalent to

Rewrite the following statement in the form "$p$ if and only if $q$":
$p:$ If you watch television,then your mind is free and if your mind is free,then you watch television.

If $p \equiv$ The switch $S_1$ is closed,$q \equiv$ The switch $S_2$ is closed,$r \equiv$ The switch $S_3$ is closed,then the symbolic form of the following switching circuit is equivalent to:

In a Boolean Algebra $B$,for all $x, y \in B$,$x \wedge (x \vee y)$ is equal 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 $x - 17 < 20$.
$S_3: \forall n \in N, x^2 + 3x - 10 = 0$.
$S_4: \forall n \in N, n^2 \ge 1$.

$\sim[(p \vee \sim q) \rightarrow (p \wedge \sim q)] \equiv$