The Boolean expression A′B′+AB′+A′B is equivalent to:
2022
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
Start by removing duplicate terms (idempotence) so the expression can be treated as: A'B' + AB' + A'B.
Factor B' from the first two terms: B'(A' + A) + A'B.
Simplify A' + A = 1, giving B' + A'B.
Use distributive/absorption: B' + A'B = (B' + A')(B' + B) = A' + B'.
Since A' + B' = (AB)', the expression equals the NAND of A and B.
Therefore the given Boolean expression is equivalent to A NAND B.