Number of switches in alternative equivalent simple circuit for the circuit is (are)

Step-by-step solution

The circuit's Boolean expression is derived from its structure, with switches S₁ , S₂ , and S₃ , and their complements where applicable. The overall function is F = S₁ (S₂' + S₃') + S₁ S₂ S₃ . Factoring S₁ , we obtain F = S₁ [(S₂' + S₃') + (S₂ S₃) ] . Since S₂' + S₃' = (S₂ S₃)' , the expression simplifies to S₁ [(S₂ S₃)' + (S₂ S₃) ] . Applying the complement law A' + A = 1 with A = S₂ S₃ , we have F = S₁ 1 = S₁ . The simplified circuit is equivalent to a single switch S₁ , so the number of switches required is 1 .