Question:
Let \(p\): switch \(S_{1}\) is closed, \(q\): switch \(S_{2}\) is closed.
Then, the equivalent symbolic form for the following circuit is:
Let \(p\): switch \(S_{1}\) is closed, \(q\): switch \(S_{2}\) is closed.
Then, the equivalent symbolic form for the following circuit is:
Then, the equivalent symbolic form for the following circuit is:
Show Hint
Series branches mean AND, parallel branches mean OR; a primed switch stands for the negation.
Updated On: Nov 12, 2026
- \(\sim p\wedge \sim q\)
- \(p\wedge q\)
- \(p\vee q\)
- \(\sim p\vee \sim q\)
Show Solution
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The Correct Option is D
Solution and Explanation
Step 1: Read the circuit
Let \(p\) and \(q\) represent switches \(S_1\) and \(S_2\). The primed switches \(S_1'\) and \(S_2'\) represent \(\sim p\) and \(\sim q\).
Step 2: Write each branch
Branch 1 is \(p\wedge\sim q\), branch 2 is \(\sim p\wedge q\), branch 3 is \(\sim p\wedge\sim q\).
Step 3: Join in parallel
\((p\wedge\sim q)\vee(\sim p\wedge q)\vee(\sim p\wedge\sim q)\)
Step 4: Simplify
These cover every case except \(p\) true and \(q\) true, so the form is \(\sim(p\wedge q)=\sim p\vee\sim q\).
Final Answer:
The circuit is equivalent to not p or not q. \[ \boxed{\text{(D) }\sim p\vee\sim q} \]
Let \(p\) and \(q\) represent switches \(S_1\) and \(S_2\). The primed switches \(S_1'\) and \(S_2'\) represent \(\sim p\) and \(\sim q\).
Step 2: Write each branch
Branch 1 is \(p\wedge\sim q\), branch 2 is \(\sim p\wedge q\), branch 3 is \(\sim p\wedge\sim q\).
Step 3: Join in parallel
\((p\wedge\sim q)\vee(\sim p\wedge q)\vee(\sim p\wedge\sim q)\)
Step 4: Simplify
These cover every case except \(p\) true and \(q\) true, so the form is \(\sim(p\wedge q)=\sim p\vee\sim q\).
Final Answer:
The circuit is equivalent to not p or not q. \[ \boxed{\text{(D) }\sim p\vee\sim q} \]
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