# Write the symbolic form of the following switching circuit construct its switching table and interpret it. - Mathematics and Statistics

Sum

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

#### 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?