The statement $(p \wedge \sim q) \wedge (\sim p \vee q)$ is a...

The negation of $\sim s \vee (\sim r \wedge s)$ is equivalent to

The symbolic form of the given switching circuit is equivalent to $..........$

If $\sim p \vee q$ is false, then which of the following is correct?

Consider the following statements:
$p$: the switch $S_1$ is closed.
$q$: the switch $S_2$ is closed.
$r$: the switch $S_3$ is closed.
Then the switching circuit represented by the statement $(p \wedge q) \vee (\sim p \wedge (\sim q \vee p \vee r))$ is

Show that the statement $p:$ "If $x$ is a real number such that $x^{3}+4x=0$,then $x$ is $0$" is true by the direct method.