The logically equivalent statement of $(\sim p \wedge q) \vee (\sim p \wedge \sim q) \vee (p \wedge \sim q)$ is

$p \rightarrow \sim q$ can also be written as

The negation of the statement " $72$ is divisible by $2$ and $3$ " is

The negation of $p \wedge (q \rightarrow \sim r)$ is

The equivalent statement of "If three vertices of a triangle are represented by cube roots of unity,then the triangle is an equilateral triangle" is

Which of the following statement patterns is a tautology?
$S_{1} \equiv \sim p \rightarrow (q \leftrightarrow p)$
$S_{2} \equiv \sim p \vee \sim q$
$S_{3} \equiv (p$ $\rightarrow q) \wedge (q$ $\rightarrow p)$
$S_{4} \equiv (q \rightarrow p) \vee (\sim p \leftrightarrow q)$