Let A’ represent complement of A. Which of the following boolean expressions is/are true?

(A) A +AB=A 

(B) (A+B)'= A'B'

(C) (A')'= A

(D) (AB)'= A'+B'

Choose the correct answer from the options given below:

Solution:

(A) \(A + AB = A(1 + B) = A \cdot 1 = A\)   (Absorption law) ✅

(B) \((A + B)' = A'B'\)   (De Morgan’s law: complement of sum is product of complements) ✅

(C) \((A')' = A\)   (Double complement law) ✅

(D) \((AB)' = A' + B'\)   (De Morgan’s law: complement of product is sum of complements) ✅

Final Answer: All are true — (A), (B), (C), (D).