Negation of the statement $(p \vee r) \Rightarrow (q \vee r)$ is :

$(S1) (p \Rightarrow q) \vee (p \wedge (\sim q))$ is a tautology. $(S2) ((\sim p) \Rightarrow (\sim q)) \wedge ((\sim p) \vee q)$ is a contradiction. Then

Write the negation of the following statement:
$s:$ There exists a number $x$ such that $0 < x < 1.$

If $q$ is false and $p \wedge q \leftrightarrow r$ is true,then which of the following is a tautology?

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

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?