Question

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

Answer 1

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.