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(C) The circuit consists of three parallel branches. The logical expression for the circuit is:$S = (S_1 \land S_2) \lor (S_1' \land S_2) \lor (S_3 \l

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(C) The circuit consists of three parallel branches. The logical expression for the circuit is:$S = (S_1 \land S_2) \lor (S_1' \land S_2) \lor (S_3 \land S_2')$Using the distributive law on the first two terms:$S = ((S_1 \lor S_1') \land S_2) \lor (S_3 \land S_2')$Since $S_1 \lor S_1' = 1$ (tautology):$S = (1 \land S_2) \lor (S_3 \land S_2')$$S = S_2 \lor (S_3 \land S_2')$Using the distributive law $A \lor (B \land C) = (A \lor B) \land (A \lor C)$:$S = (S_2 \lor S_3) \land (S_2 \lor S_2')$Since $S_2 \lor S_2' = 1$:$S = S_2 \lor S_3$This simplified circuit requires only two switches, $S_2$ and $S_3$, connected in parallel.

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

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