The minimum number of switches in the simplif | vedclass

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(C) Let $S_1, S_2, S_3$ be the switches. The circuit consists of three parallel branches.Branch $1$: $S_1$ and $S_2$ in series $\rightarrow (S_1 \land

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$2$

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(C) Let $S_1, S_2, S_3$ be the switches. The circuit consists of three parallel branches.Branch $1$: $S_1$ and $S_2$ in series $\rightarrow (S_1 \land S_2)$Branch $2$: $S_1'$ and $S_2$ in series $\rightarrow (S_1' \land S_2)$Branch $3$: $S_3$ and $S_2'$ in series $\rightarrow (S_3 \land S_2')$The total circuit expression is $C = (S_1 \land S_2) \lor (S_1' \land S_2) \lor (S_3 \land S_2')$.Using the distributive law on the first two terms: $(S_1 \lor S_1') \land S_2 \lor (S_3 \land S_2')$.Since $(S_1 \lor S_1') = T$ (a tautology), the expression becomes $T \land S_2 \lor (S_3 \land S_2')$.This simplifies to $S_2 \lor (S_3 \land S_2')$.Using the distributive law again: $(S_2 \lor S_3) \land (S_2 \lor S_2')$.Since $(S_2 \lor S_2') = T$, the expression simplifies to $(S_2 \lor S_3)$.This represents two switches $S_2$ and $S_3$ in parallel. The minimum number of switches is $2$.

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

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