The Boolean expression A′B′ + AB′ + A′B is equivalent to:
2023
The Boolean expression A′B′ + AB′ + A′B is equivalent to:
- A.
A NAND B
- B.
A NOR B
- C.
A XOR B
- D.
A OR B
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Correct answer: A
Simplified result: The expression is equivalent to A NAND B, i.e., (A B)'. Steps: Start with F = A'B' + AB' + A'B
Factor B' from the first two terms: F = B'(A' + A) + A'B
Since A' + A = 1, F = B' + A'B
Use distributive/absorption: B' + A'B = (B' + A')(B' + B) = A' + B'
By De Morgan, A' + B' = (A B)'. Therefore F = (A B)', which is A NAND B.
Quick truth-check: inputs (A,B)