The logical expression $[p \wedge (q \vee r)] \vee [\sim r \wedge \sim q \wedge p]$ is equivalent to

The logical expression $[p \wedge (q \vee r)] \vee [(\sim p \wedge q) \vee (\sim p \wedge r)]$ is equivalent to

If $P$ and $Q$ are two statements,then which of the following compound statements is a tautology?

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 statement patterns is a tautology?

The statement pattern $(\sim p \wedge q)$ is logically equivalent to