$\sim (p \vee q) \vee (\sim p \wedge q)$ is logically 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

If the truth value of the Boolean expression $((p \vee q) \wedge (q$ $\rightarrow r) \wedge (\sim r))$ $\rightarrow (p \wedge q)$ is false,then the truth values of the statements $p, q, r$ respectively can be:

$\sim (p \Rightarrow q) \Leftrightarrow \sim p \vee \sim q$ is

If $p : 5$ is not greater than $2$ and $q : \text{Jaipur is the capital of Rajasthan}$ are two statements,then the negation of the statement $p \Rightarrow q$ is:

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