Question

If the symbolic form of the switching circuit is \( \sim p \vee ( p \wedge \sim q) \vee q \), then the current flows through the circuit only if:

• A. irrespective of the status of the switches
• B. one switch should be open and the other should be closed
• C. both switches should be closed
• D. both switches should be open

Hint:

In logic circuits, a disjunction (\( \vee \)) means that the current will flow if any of the conditions is satisfied.

Answer 1

The Correct Option is A

Step 1: Analyze the given symbolic expression.
The given circuit expression is \( \sim p \vee ( p \wedge \sim q) \vee q \). This is a combination of negations, conjunctions, and disjunctions. Step 2: Simplify the expression.
First, simplify the expression: \[ \sim p \vee ( p \wedge \sim q) \vee q \] This can be interpreted as "the current flows if either switch \( p \) is open, or if switch \( p \) is closed and switch \( q \) is open, or if switch \( q \) is closed". Step 3: Conclusion.
Thus, the current flows through the circuit irrespective of the status of the switches. Therefore, the correct answer is \( \boxed{\text{irrespective of the status of the switches}} \).