Question

What will be the output after minimizing the following expression with the help of a K-map? \[ F(X,Y) = X Y + X Y' + X Y \]

• A. X
• B. X + Y
• C. X Y
• D. Y

Hint:

When minimizing Boolean expressions, use the consensus theorem to simplify terms involving both \( X \) and \( X' \).

Answer 1

The Correct Option is B

Step 1: Expression Simplification.
The initial expression is \( F(X,Y) = X Y + X Y' + X Y \). Recognizing that \( X Y + X Y = X \), the expression simplifies to: \[F(X,Y) = X + X Y'\]

Step 2: Applying Consensus Theorem.
Applying the consensus theorem, which states \( X + X Y' = X + Y \), yields the simplified expression: \[F(X,Y) = X + Y\]

Step 3: Final Result.
The minimized expression is \( X + Y \). Therefore, option (B) is the correct answer.