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, represented by $S_1 \l

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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, represented by $S_1 \land S_2$.Branch $2$: $S_1'$ and $S_2$ in series, represented by $S_1' \land S_2$.Branch $3$: $S_3$ and $S_2'$ in series, represented by $S_3 \land S_2'$.The total circuit is the parallel combination of these branches:$L = (S_1 \land S_2) \lor (S_1' \land S_2) \lor (S_3 \land S_2')$Using the distributive law on the first two terms:$L = ((S_1 \lor S_1') \land S_2) \lor (S_3 \land S_2')$Since $S_1 \lor S_1' = T$ (a tautology, always closed):$L = (T \land S_2) \lor (S_3 \land S_2')$$L = S_2 \lor (S_3 \land S_2')$Using the distributive law again:$L = (S_2 \lor S_3) \land (S_2 \lor S_2')$Since $S_2 \lor S_2' = T$:$L = S_2 \lor S_3$This simplified circuit requires $2$ switches ($S_2$ and $S_3$).

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

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