The statement pattern $[(p \land q) \to (\sim p \lor r)] \lor [(\sim p \lor r) \to (p \land q)]$ is

The negation of the statement "If an integer is greater than $4$ and less than $5$, then it is a multiple of $3$" is:

Let $*, \square \in \{\wedge, \vee\}$ be such that the Boolean expression $(p * \sim q) \Rightarrow (p \square q)$ is a tautology. Then :

For any two statements $p$ and $q,$ the negation of the expression $p \vee ( \sim p \wedge q)$ is

$\sim (p \vee (\sim q))$ is equal to .......

Which of the following statement patterns is a tautology?
$S_1 \equiv (\sim q \wedge p) \wedge q$
$S_2 \equiv [p \wedge (p$ $\rightarrow q)]$ $\rightarrow q$
$S_3 \equiv (p \wedge q) \wedge (\sim p \vee \sim q)$
$S_4 \equiv (p \wedge q) \rightarrow r$