Question

The symbolic form of the following circuit is (where \( p, q \) represents switches \( s_1 \) and \( s_2 \) closed respectively)

• A. \( (p \land q) \land (\sim p \land \sim q) \equiv \ell \)
• B. \( p \lor [ q \land (\sim p \land \sim q)] \equiv \ell \)
• C. \( p \land [ q \land (\sim p \land \sim q)] \equiv \ell \)
• D. \( (p \lor q) \lor (\sim p \land \sim q) \equiv \ell \)

Hint:

In Boolean algebra, always break down the logical gates and apply the basic laws (like De Morgan's Law) to simplify the expression.

Answer 1

The Correct Option is D

Step 1: Understanding the circuit.
The circuit described consists of switches \( s_1 \) and \( s_2 \), and we need to find its symbolic representation.

Step 2: Analyzing the logic gates.
The circuit involves a logical OR gate and AND gate, and the correct symbolic expression needs to be derived based on how the switches are connected.

Step 3: Conclusion.
The correct symbolic form of the circuit is \( (p \lor q) \lor (\sim p \land \sim q) \equiv \ell \), which makes option (D) the correct answer.