$\sim p \wedge q$ is logically equivalent to

The correct simplified circuit diagram for the logical statement $[\{q \wedge (\sim q \vee r)\} \wedge \{\sim p \vee (p \wedge \sim r)\}] \vee (p \wedge r)$ where $p, q, r$ represent switches $S_1, S_2, S_3$ respectively.

Which of the following Boolean expressions is not a tautology?

If the truth value of the statement pattern $[p \wedge \sim r] \rightarrow [\sim r \wedge q]$ is False,then which of the following has truth value False?

The logical statement $(p \wedge \sim q) \vee q \vee (\sim p \wedge q)$ is equivalent to

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