1.

Check whether the following switching circuits are logically equivalent – Justify.(A) (i)(ii)(B) (i) (ii)

Answer»

(A) Let p : the switch S1 is closed 

q : the switch S2 is closed 

r : the switch S3 is closed 

(A) The symbolic form of the given switching circuits are :

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.

(B) 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.



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