Question

The symbolic form of the following circuit is (where \( p, q, r \) represent switches \( s_1, s_2, s_3 \) which are closed respectively)

• A. \( (p \vee q) \wedge [\neg p \vee ( \neg q \wedge p \wedge r)] \equiv \ell \)
• B. \( [(p \vee q) \wedge \neg p] \vee [\neg p \vee q \vee r] \equiv \ell \)
• C. \( (p \wedge q) \vee [\neg p \wedge (\neg q \vee p \vee r)] \equiv \ell \)
• D. \( (p \wedge q) \vee \neg p \vee [\neg p \vee p \vee r] \equiv \ell \)

Hint:

In symbolic logic for circuits, carefully translate the behavior of each switch and gate into logical expressions using AND, OR, and NOT operators.

Answer 1

The Correct Option is C

Step 1: Understand the logic of the circuit.
The symbolic form of the circuit represents the logic gates for switches \( s_1, s_2, s_3 \), which are closed when the respective switches are true. By analyzing the circuit and simplifying the expressions for the states of the switches, we arrive at the correct logical expression for the circuit.

Step 2: Conclusion.
The correct symbolic form is \( (p \wedge q) \vee [\neg p \wedge (\neg q \vee p \vee r)] \equiv \ell \), corresponding to option (C).