The contrapositive statement of the statement "If $x$ is a prime number,then $x$ is odd" is

Identify the type of "Or" used in the following statement and check whether the statement is true or false:
$\sqrt{2}$ is a rational number or an irrational 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?

The contrapositive of "If $x$ and $y$ are integers such that $x y$ is odd,then both $x$ and $y$ are odd" is

The negation of the contrapositive of the statement pattern $(p \vee \sim q) \rightarrow (p \wedge \sim q)$ is

If a statement $q$ has truth value $False$ and $(p \wedge q) \leftrightarrow r$ has truth value $True$,then which of the following has truth value $True$?