Question

Construct the simplified circuit for the following circuit:

Answer 1

Let p : switch S₁ is closed
     q : switch S₂ is closed
      r : switch S₃ is closed
  ~ p : switch S₁ is open
  ~ q : switch S₂ is open
   ~ r : switch S₃ is open
The symbolic form of the given circuit
[p ∧ (q ∨ r)] ∨ [~ r ∧ ~ q ∧ p] 
= p ∧ [(q ∨ r) ∨ (~ q ∧ ~ r) ….(Distributive law)
= p ∧ [(q ∨ r) ∨ ~ (q  r)] ….(De Morgan’s law)
= p ∧ T ….(Compliment law)
= p ….(Identity law)
The new simplified circuit is