Question

Check whether the following switching circuits are logically equivalent - Justify.

(i)

(ii)

Answer 1

Let p: the switch S₁ is closed
      q: the switch S₂ is closed
       r: the switch S₃ is closed
The symbolic form of the given switching circuits are 
(p ∨ q) ∧ (p ∨ r) and p ∨ (q ∧ r)
By Distributive Law,
p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r)
Hence, the given switching circuits are logically equivalent.