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: Simplification of Expression.
The given expression is \( F(X,Y) = X Y + X Y' + X Y \). Observe that \( X Y + X Y = X \), so the expression simplifies to: \[ F(X,Y) = X + X Y' \]

Step 2: Using Consensus Theorem.
Now, apply the consensus theorem, which states that \( X + X Y' = X + Y \). Thus, the simplified expression is: \[ F(X,Y) = X + Y \]

Step 3: Conclusion.
The output of the minimized expression is \( X + Y \), so the correct answer is (B).