In a switching circuit, if the combination $(S_1 \wedge S_2)$ is connected in parallel to the combination $(S_1' \wedge S_2')$, then the room is lit only when $\ldots$

If the truth value of the statement pattern $(\sim p \wedge q) \vee (\sim p \wedge \sim q) \vee (p \wedge \sim q)$ is $F$, then the truth values of $(p \vee \sim q)$ and $(p \to q)$ are $\ldots$ respectively.

The minimum number of switches in the simplified form of the following switching circuit is

The correct logical equivalence from the following is /are ___
(I) $p \to (q \to r) \equiv (p \wedge q) \to r$
(II) $(p \to q) \to r \equiv p \to (q \vee r)$
(III) $(p \to q) \to r \equiv (p \to r) \wedge (\sim q \to r)$
(IV) $p \to (q \to r) \equiv q \to (p \to r)$