# Represent the following switching circuit in symbolic form and construct its switching table. Write your conclusion from the switching table. - Mathematics and Statistics

Sum

Represent the following switching circuit in symbolic form and construct its switching table. Write your conclusion from the switching table.

#### 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 table, the ‘final column’ and the column of p are identical. Hence, the given circuit is equivalent to the simple circuit with only one switch S1.
∴ the simplified form of the given circuit is:

Concept: Application of Logic to Switching Circuits
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#### APPEARS IN

Balbharati Mathematics and Statistics 1 (Arts and Science) 12th Standard HSC Maharashtra State Board
Chapter 1 Mathematical Logic
Miscellaneous Exercise 1 | Q 17 | Page 35