Maharashtra State BoardHSC Arts 12th Board Exam
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Express the following circuit in the symbolic form of logic and writ the input-output table. - Mathematics and Statistics

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Sum

Express the following circuit in the symbolic form of logic and writ the input-output table.

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Solution

Let p: the switch S1 is closed
      q: the switch S2 is closed
       r: the switch S3 is closed
  ∼ p: the switch S1′ is closed or the switch S1 is open
  ∼ q: the switch S2′ is closed or the switch S2 is open
   ∼ r: the switch S3′ is closed or the switch S3 is open
       l: the lamp L is on

The symbolic form of the given circuit is:
(∼ p ∧ q) ∨ (p ∧ ∼ q)

Input-Output Table

q ∼ p ∼ q ∼ p ∧ q p ∧ ∼ q (∼ p ∧ q) ∨ (p ∧ ∼ q)
1 1 0 0 0 0 0
1 0 0 1 0 1 1
0 1 1 0 1 0 1
0 0 1 1 0 0 0
Concept: Application of Logic to Switching Circuits
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