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.

For each of the following compound statements,first identify the corresponding component statements. Then check whether the statements are true or not.
If a triangle $ABC$ is equilateral,then it is isosceles.

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

If $p$: It is raining and $q$: It is pleasant,then the symbolic form of "It is neither raining nor pleasant" is

Which of the following logical statements is a tautology?

Negation of the inverse of the following statement pattern $(p \wedge q) \rightarrow (p \vee \sim q)$ is