Question
Download Solution PDFWhich of the following Boolean algebra rules is correct ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFThe correct answer is option 4: A + A̅B = A + B
Key Points
- A + A̅B = A + B is a valid Boolean identity derived using the Distributive Law and the Law of Complementation.
- It is a known simplification rule in Boolean algebra.
- Proof:
- A + A̅B = (A + A̅)(A + B) (Distributive Law)
- (A + A̅) = 1 (Complement Law)
- ⇒ 1.(A + B) = A + B
Additional Information
- Option 1 – A.A̅ = 1: ❌ Incorrect. A.A̅ = 0 (by Complement Law)
- Option 2 – A + AB = A + B: ❌ Incorrect. A + AB = A (by Absorption Law)
- Option 3 – A(A + B) = B: ❌ Incorrect. A(A + B) = A (by Absorption Law)
Hence, the correct answer is: option 4: A + A̅B = A + B
Last updated on Jul 3, 2025
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