Question

Evaluate the expression: (X + Z)(X + XZ’) + XY + Y.

(a) XY+Z’

(b) Y+XZ’+Y’Z

(c) X’Z+Y

(d) X+Y

This question was addressed to me in an interview for internship.

The above asked question is from Minimization of Boolean Functions in division Boolean Algebra and Modeling Computations of Discrete Mathematics

Answer 1

The correct answer is (d) X+Y

For explanation: (X + Z)(X + XZ’) + XY + Y      [Original Expression]

= (x + z)X(1 + Z’) + XY + Y   [Distributive]  

= (X + Z)X + XY + Y              [Complement, Identity]

= (X+Z)X + Y(X+1)  [ Distributive]

= (X+Z)X + Y            [Idempotent]

= XX + XZ + Y  [Distributive]

= X + XZ + Y               [Identity]

= X(1+Z) + Y

= X + Y   [Idempotent].