The statement pattern $(p \wedge q) \vee (\sim p \wedge q) \vee (r \wedge \sim q)$ is logically 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.

Which one of the following is the pair of equivalent circuits?
$i. (p \land q) \lor (p \land r)$
$ii. p \lor (q \land r)$
$iii. p \land (q \lor r)$
$iv. p \land q \land r$
$v. (p \land q) \lor r$

If $(p \wedge \sim r) \rightarrow (\sim p \vee q)$ has a truth value of $False$,then the truth values of $p, q, r$ are respectively:

The contrapositive of the statement $\sim p \vee (q \wedge \sim r)$ is

Write the negation of the following statement:
$p:$ For every real number $x, x^{2} > x.$