The negation of the Boolean expression $p \vee (\sim p \wedge q)$ is equivalent to

The number of choices of $\Delta \in \{\wedge, \vee, \Rightarrow, \Leftrightarrow\}$,such that $(p \Delta q) \Rightarrow ((p \Delta \sim q) \vee ((\sim p) \Delta q))$ is a tautology,is

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

What type of statement is $\sim (p \rightarrow q) \Leftrightarrow (\sim p \vee \sim q)$?

The Boolean expression $(p \wedge \sim q) \vee q \vee (\sim p \wedge q)$ is equivalent to:

If statements $p$ and $q$ are true and $r$ and $s$ are false,then the truth values of $\sim(p \rightarrow q) \leftrightarrow (p \wedge s)$ and $(\sim p \rightarrow q) \wedge (r \leftrightarrow s)$ are respectively: