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 is p ∧ (q ∨ r) and (p ∧ q) ∨ (p ∧ r) respectively.
By Distributive Law, p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r)
Hence, the given switching circuits are logically equivalent.