The Boolean expression AB+AB′+A′C+AC is independent of Boolean variable ______.
2023
The Boolean expression AB+AB′+A′C+AC is independent of Boolean variable ______.
- A.
A
- B.
B
- C.
C
- D.
More than one of the above
- E.
None of the above
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Show answer & explanation
Correct answer: B
Step 1: Start with the given Boolean expression: AB + AB′ + A′C + AC. Step 2: Factor out A from the first two terms: AB + AB′ = A(B + B′). Step 3: Since B + B′ = 1, this simplifies to A(1) = A. Step 4: Now the expression becomes A + A′C + AC. Step 5: Factor out C from the last two terms: A′C + AC = C(A′ + A). Step 6: Since A′ + A = 1, this simplifies to C(1) = C. Step 7: The expression now is A + C. Step 8: The simplified expression A + C does not contain B, so the original expression is independent of B.