The statement pattern $(\sim p \wedge q)$ is logically equivalent to

The negation of the converse of the statement $p \lor q$ is:

Which of the following is logically equivalent to $(p \wedge q)$?

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

Rewrite the following statement in the form "$p$ if and only if $q$":
$r:$ If a quadrilateral is equiangular,then it is a rectangle and if a quadrilateral is a rectangle,then it is equiangular.

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.