Question

Express the following circuit in the symbolic form of logic and writ the input-output table.

Answer 1

Let p: the switch S₁ is closed
      q: the switch S₂ is closed
       r: the switch S₃ 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
   ∼ r: the switch S₃′ is closed or the switch S₃ is open
       l: the lamp L is on

The symbolic form of the given circuit is:
p ∨ (q ∧ r) ≡ l
l is generally dropped and it can be expressed as:
p ∨ (q ∧ r)

Input-Output Table

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