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)] ∨ (∼ q ∧ ∼ r)

Input-Output Table

p	q	r	∼q	∼r	∼q∨r	p∧(∼q∨r)	∼q∧∼r	[p∧(∼q∨r)] ∨ (∼q∧∼r)
1	1				1	1	0	1
1	1				0	0	0	0
1	0				1	1	0	1
1	0				1	1	1	1
0	1				1	0	0	0
0	1				0	0	0	0
0	0				1	0	0	0
0	0				1	0	1	1