The simplest form of the following switching | vedclass

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(C) Let $S_1$ and $S_2$ be the switches. The circuit consists of three parallel branches. The symbolic representation is:$L = (S_1 \land S_2) \lor (S_

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(C) Let $S_1$ and $S_2$ be the switches. The circuit consists of three parallel branches. The symbolic representation is:$L = (S_1 \land S_2) \lor (S_1 \land S_2') \lor (S_1' \land S_2)$Using the distributive law on the first two terms:$L = (S_1 \land (S_2 \lor S_2')) \lor (S_1' \land S_2)$Since $(S_2 \lor S_2') = 1$ (tautology):$L = (S_1 \land 1) \lor (S_1' \land S_2)$$L = S_1 \lor (S_1' \land S_2)$Using the distributive law $A \lor (B \land C) = (A \lor B) \land (A \lor C)$:$L = (S_1 \lor S_1') \land (S_1 \lor S_2)$Since $(S_1 \lor S_1') = 1$:$L = 1 \land (S_1 \lor S_2) = S_1 \lor S_2$This corresponds to two switches $S_1$ and $S_2$ in parallel.

The simplest form of the following switching circuit is:

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