The Boolean expression \(AB+A \overline{B}+\overline{A}C+AC\) is unaffected by…
2019
The Boolean expression \(AB+A \overline{B}+\overline{A}C+AC\) is unaffected by the value of the Boolean variable _________.
- A.
\(A\) - B.
\(B\) - C.
\(C\) - D.
\(A, B \ and \ C\)
Attempted by 363 students.
Show answer & explanation
Correct answer: B
Solution: Simplify the expression AB + A B' + A' C + A C.
Factor A from the first two terms: AB + A B' = A(B + B') = A because B + B' = 1.
Substitute that result into the expression: A + A' C + A C.
Use the identity A + A' C = A + C (consensus/absorption). Also A + A C = A, so overall the expression reduces to A + C.
Final simplified expression: A + C
Conclusion: The simplified form A + C does not contain B, so the value of B does not affect the expression. Therefore the expression is unaffected by the variable B.
A video solution is available for this question — log in and enroll to watch it.