Question

The reduced form of the Boolean function \( F = xyz + xyz' + x'yz + zy'z \) is

• A. \( xy + yz + xz \)
• B. \( x + yz + xz \)
• C. \( x + y + z \)
• D. \( xy + yz + xz \)

Hint:

Use the identity \( x + x' = 1 \) and \( y + y' = 1 \) to simplify Boolean expressions efficiently.

Answer 1

The Correct Option is D

Let's simplify the Boolean expression step by step: \[ F = xyz + xyz' + x'yz + zy'z \] We can factor terms: \[ F = xz(y + y') + yz(x' + x) \] Using the identity \( y + y' = 1 \) and \( x + x' = 1 \), we get: \[ F = xz(1) + yz(1) \] \[ F = xz + yz \] Thus, the reduced form of the Boolean function is \( \boxed{xy + yz + xz} \).