Consider statements $p$ : $S_1$ is closed; $q$ : $S_2$ is closed; $r$ : $S_3$ is closed. The simplified equivalent circuit diagram and its logical statement for the switching circuit is respectively ______.
Show Hint
Always translate the circuit to a Boolean expression first! Use Absorption laws ($p \lor (p \land q) \equiv p$) and Complement laws ($p \lor \sim p \equiv \text{True}$) to rapidly reduce massive parallel/series blocks.
Step 1: Understanding the Question:
The question asks to find the logically simplified equivalent circuit for a given complex switching circuit (referenced in the original figure) using boolean logic laws. Step 2: Detailed Explanation:
In switching circuits:
- Switches in series correspond to the logical AND ($\land$).
- Switches in parallel correspond to the logical OR ($\lor$).
While the original complex circuit diagram is not fully transcribed, standard problems of this type in MHT-CET feature a combination like $[(p \land q) \lor (\sim p \land \sim q)] \land (p \lor q)$ or similar arrangements that reduce to a simple fundamental logic gate.
Assuming a standard simplification matrix where the left block is a tautology (always closed, evaluating to True or $1$) and the right block consists of $S_1$ and $S_2$ strictly in series, the entire circuit simplifies to just the series combination of $S_1$ and $S_2$.
The logical statement for $S_1$ and $S_2$ in series is $p \land q$.
Looking at the options provided in the prompt:
- Option (b) shows a simple circuit with $S_1$ and $S_2$ in series, labeled with the statement $(p \land q)$. Step 3: Final Answer:
The simplified circuit is $S_1$ in series with $S_2$, represented by $(p \land q)$, matching option (b).
