The following statement $(p \to q) \to [(\sim p \to q) \to q]$ is

Consider the following statements:
$p$: If voltage increases, then current decreases.
$q$: If voltage does not increase, then current does not decrease.
$r$: If current decreases, then voltage increases.
$s$: If current does not decrease, then voltage does not increase.
Which of the following pairs of statements have the same meaning?

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

Which of the following statements is a tautology?

What is the statement $(p \wedge q) \rightarrow p$?

Which of the following is not logically equivalent to the proposition: "$A$ real number is either rational or irrational"?