Simplify the following Boolean Expression? (1 + A).(A + B).(A' + B)
2021
Simplify the following Boolean Expression?
(1 + A).(A + B).(A' + B)
- A.
B
- B.
AB
- C.
A'B
- D.
A+B
Attempted by 138 students.
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Correct answer: A
First, simplify (1 + A) using the Annulment Law: 1 + A = 1.
The expression reduces to (A + B)(A' + B). Expanding this gives AA' + AB + A'B + BB.
Apply Boolean laws: AA' = 0 and BB = B. The expression becomes AB + A'B + B.
Factor out B: B(A + A') + B. Since (A + A') = 1, this simplifies to B(1) + B.
Using the Idempotent Law (B + B = B), the final simplified expression is B.