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
  ∼ p: the switch S1‘ is closed or the switch S1 is open.
  ∼ q: the switch S2′ is closed or the switch S2 is open.
Then the symbolic form of the given circuit is:
p ∨ (∼ p ∧ ∼ q) ∨ (p ∧ q)

Switching Table

p q ∼p  ∼q ∼p∧∼q p∧q p∨(∼p∧∼q)∨(p∧q)
1 1 0 0 0 1 1
1 0 0 1 0 0 1
0 1 1 0 0 0 0
0 0 1 1 1 0 1

Since the final column contains ‘0’ when p is 0 and q is ‘1’, otherwise it contains ‘1’.
Hence, the lamp will not glow when S1 is OFF and S2 is ON, otherwise, the lamp will glow.

Concept: Application of Logic to Switching Circuits
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