Question

Give an alternative equivalent simple circuit for the following circuit:

Answer 1

Let p: the switch S₁ is closed
     q: the switch S₂ is closed
 ∼ p: the switch S₁′ is closed or the switch S₁ is open
Then the symbolic form of the given circuit is
p ∧ (∼ p ∨ q).
Using the laws of logic, we have,
p ∧ (∼ p ∨ q)
≡ (p ∧ ∼ p) ∨ (p ∧ q) .........(By Distributive Law)
≡ F ∨ (p ∧ q) ...........(By Complement Law)
≡ p ∧ q .........(By Identity Law)
Hence, the alternative equivalent simple circuit is: