The boolean expression AB + AB'+ A'C + AC is independent of the boolean variable

To determine which variable the expression is independent of, we simplify the boolean function F = AB + AB' + A'C + AC. First, factor out A from the first two terms: A(B + B'). Since (B + B') = 1, this simplifies to A. Next, factor out C from the last two terms: C(A' + A). Since (A' + A) = 1, this simplifies to C. Combining these results gives F = A + C. The simplified expression contains only variables A and C, meaning the output does not change regardless of the value of B. Therefore, the expression is independent of variable B. Options A and C are incorrect because both appear in the final simplified form F = A + C.