The negation of the conditional statement,"If it rains,$I$ shall go to school" is:

The negation of $(p \land q) \to ((p \lor r) \to \sim q)$ 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?

Write the negation of the following statement and check whether the resulting statement is true:
Australia is a continent.

If the statements $p, q$ and $r$ have the truth values $F, T, F$ respectively,then the truth values of the statement patterns $(p \wedge \sim q) \rightarrow r$ and $(p \vee q) \rightarrow r$ are respectively

If $p$ and $q$ are true statements and $r$ is a false statement,then which of the following is correct?