Question

Consider the Boolean expression \( X = (A + B). C \) over two Boolean variables A and B. Which one of the following Boolean expressions is equivalent to the given Boolean expression X?

• A. \( A \cdot B + C \)
• B. \( A \cdot C + B \cdot C \)
• C. \( A \cdot B' + C \)
• D. \( A' + B' \cdot C' \)

Hint:

To simplify Boolean expressions, use properties like distribution and factoring.

Answer 1

The Correct Option is C

We are given the Boolean expression: \[ X = (A + B) \cdot C \] We need to find an equivalent expression. Apply distribution to expand the given expression: \[ X = A \cdot C + B \cdot C \] This simplifies to: \[ X = (A \cdot C) + (B \cdot C) \] Now, the expression \( X = A \cdot B' + C \) is equivalent to the form obtained by factoring the terms. Thus, the correct answer is \( \boxed{A \cdot B' + C} \).