$ \sim[(\sim p) \wedge q] $ is logically equivalent to

$\sim ((\sim p) \wedge q)$ is equivalent to

Which of the following statement patterns is a tautology?

Write the negation of the following statement:
$\sqrt{7}$ is rational.

If the truth value of the expression $[(p \vee q) \wedge (q$ $\rightarrow r) \wedge (\sim r)]$ $\rightarrow (p \wedge q)$ is False,then the truth values of $p, q, r$ are respectively:

Let $\Delta, \nabla \in \{\wedge, \vee\}$ be such that $( p \rightarrow q ) \Delta ( p \nabla q )$ is a tautology. Then