Question:
The switching circuit for the logical expression \((p\wedge q)\vee \sim (p\wedge q)\) is simplified and found to be equivalent to a circuit with:
The switching circuit for the logical expression \((p\wedge q)\vee \sim (p\wedge q)\) is simplified and found to be equivalent to a circuit with:
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The expression is of the form r or not r, which is always true, so the circuit is always closed.
Updated On: Nov 12, 2026
- Two switches in series
- Two switches in parallel
- A single switch
- The lamp always glows
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept
In a switching circuit, a true statement means a closed switch and a false statement means an open switch.
Step 2: Simplify
Let \(r=p\wedge q\). The expression becomes \(r\vee\sim r\).
Step 3: Use the complement law
\(r\vee\sim r\) is a tautology, so it is always true.
Step 4: Interpret
An always true expression means current always flows, so the lamp always glows.
Final Answer:
The lamp always glows. \[ \boxed{\text{(D) }\text{The lamp always glows}} \]
In a switching circuit, a true statement means a closed switch and a false statement means an open switch.
Step 2: Simplify
Let \(r=p\wedge q\). The expression becomes \(r\vee\sim r\).
Step 3: Use the complement law
\(r\vee\sim r\) is a tautology, so it is always true.
Step 4: Interpret
An always true expression means current always flows, so the lamp always glows.
Final Answer:
The lamp always glows. \[ \boxed{\text{(D) }\text{The lamp always glows}} \]
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