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

The logical statement $(p$ $\rightarrow q) \wedge (p$ $\rightarrow \sim p)$ is equivalent to

The contrapositive of the statement "If $x \in A$ or $x \in B$,then $x \in A \cup B$" is:

Show that the statement "For any real numbers $a$ and $b$,$a^{2}=b^{2}$ implies that $a=b$" is not true by giving a counter-example.

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?

Which of the following is not true?