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

The statement pattern $(p \wedge q) \wedge [(p \wedge q) \vee (\sim p \wedge q)]$ is equivalent to

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 method of contrapositive.

If the truth value of the compound statement $[(p \leftrightarrow q) \land (q \to r) \land \sim r] \to (p \land \sim q)$ is false, then the truth values of the statement patterns $(p \to q) \leftrightarrow (q \to r)$ and $\sim (p \lor r) \to (q \land p)$ are, respectively ...

The number of choices of $\Delta \in \{\wedge, \vee, \Rightarrow, \Leftrightarrow\}$,such that $(p \Delta q) \Rightarrow ((p \Delta \sim q) \vee ((\sim p) \Delta q))$ is a tautology,is

If the symbolic form of the switching circuit is $[\sim p \vee (p \wedge \sim q)] \vee q$,then the current flows through the circuit only if