Question

A Boolean function \( X \) is given as \( X = AB + AC \). The reduced form of \( X \) is:

• A. \( A + B + C \)
• B. \( A(B + C) \)
• C. \( A + B + C \)
• D. \( B + AC \)

Hint:

In Boolean algebra, use the distributive law \( AB + AC = A(B + C) \) to simplify expressions quickly. It helps reduce gate count in logic circuit design.

Answer 1

The Correct Option is B

Step 1: Given Boolean expression \[ X = AB + AC \] Step 2: Apply the Distributive Law: The distributive law of Boolean algebra states that: \[ AB + AC = A(B + C) \] Step 3: Hence, the reduced form of the Boolean function is: \[ X = A(B + C) \]