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

Which of the following Boolean expressions is a tautology?

If $P \Rightarrow (q \vee r)$ is false,then the truth values of $p, q, r$ are respectively

The symbolic form of the given switching circuit is equivalent to $..........$

$S_1$: If $-7$ is an integer,then $\sqrt{-7}$ is a complex number.
$S_2$: $-7$ is not an integer or $\sqrt{-7}$ is a complex number.

Consider the following statements:
$p: 2$ is an even prime number.
$q: \text{If } z_1 = 2 - i, z_2 = -2 + i \text{ where } i = \sqrt{-1}, \text{ then } \operatorname{Im}\left[\frac{1}{z_1 \bar{z}_2}\right] = -\frac{1}{5}$.
$r: \tan(-945^{\circ}) = -1$.
Which of the following has a truth value of True?