Maharashtra State BoardHSC Arts 12th Board Exam
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Write the symbolic form of the following switching circuit construct its switching table and interpret it. - Mathematics and Statistics

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Sum

Write the symbolic form of the following switching circuit construct its switching table and interpret it.

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Solution

Let p: the switch S1 is closed
      q: the switch S2 is closed
      r: the switch S3 is closed
 ∼ q: the switch S2′ is closed or the switch S2 is open
  ∼ r: the switch S3′ is closed or the switch S3 is open
Then the symbolic form of the given circuit is:
[p ∨ (∼ q) ∨ (∼ r)] ∧ [p ∨ (q ∧ r)]

Switching Table

p q r ∼q ∼r p∨(∼q)∨(∼r) q∧r p∨(q∧r) Final column
          (I)   (II) (I) ∧ (II)
1 1 1 0 0 1 1 1 1
1 1 0 0 1 1 0 1 1
1 0 1 1 0 1 0 1 1
1 0 0 1 1 1 0 1 1
0 1 1 0 0 0 1 1 0
0 1 0 0 1 1 0 0 0
0 0 1 1 0 1 0 0 0
0 0 0 1 1 1 0 0 0

From the switching table, the ‘final column’ and the column of p are identical. Hence, the lamp will glow which S1 is ‘ON’.

Concept: Application of Logic to Switching Circuits
  Is there an error in this question or solution?

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