Let $a: \sim(p \wedge \sim r) \vee(\sim q \vee s)$ and $b: (p \vee s) \leftrightarrow(q \wedge r)$. If the truth values of $p$ and $q$ are $T$ and that of $r$ and $s$ are $F$,then the truth values of $a$ and $b$ are respectively...

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

Let $p$ be the statement '$x$ is an irrational number',$q$ be the statement '$y$ is a transcendental number',and $r$ be the statement '$x$ is a rational number or $y$ is a transcendental number'.
Statement-$1$: $r$ is equivalent to $q \lor p$.
Statement-$2$: $r$ is equivalent to $(p \Leftrightarrow \sim q)$.

Statement $-1 :$ $\sim (p \leftrightarrow \sim q)$ is equivalent to $p \leftrightarrow q$.
Statement $-2 :$ $\sim (p \leftrightarrow \sim q)$ is a tautology.

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?

The statement pattern $[(p$ $\rightarrow q) \wedge \sim q]$ $\rightarrow r$ is a tautology when $r$ is equivalent to