MHT CET · Maths · Mathematical Reasoning

If the symbolic form of the switching circuit is \([\sim \mathrm{pv}(\mathrm{p} \wedge \sim \mathrm{q})] \mathrm{v} \mathrm{q}\), then the current flows through the circuit onlyif

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

Verified Solution

Answer & Solution

Correct Answer

(A) irrespective of status of the switches

Step-by-step Solution

Detailed explanation

\([\sim p \vee(p \wedge \sim q)] \vee q\)
\(=[(\sim p \vee p) \wedge(\sim p \vee \sim q)] \vee q\)
\(E[T \wedge(\sim p \vee \sim q)] \vee q\)
\(\equiv(\sim p \vee \sim q) \vee q\)
\(\equiv \sim p \vee(\sim q \vee q) \equiv \sim p \vee T \equiv T\)
This shows that current flows irrespective of status of the switches.

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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