Question

Given the function F(X, Y, Z) = XZ + Z(X’ + XY), the equivalent most simplified Boolean representation for F is :

(a)  Z + YZ

(b)  Z + XYZ

(c)  XZ

(d)  X + YZ

(e)  None of these

Answer 1

XZ + Z(X'+ XY)= XZ + X’Z + XYZ   (distributive Law)

= Z(X+X’) + XYZ    (distributive Law)

= Z(1) + XYZ       (Complementarity Law)

= Z+XYZ (Identity Law)

The equivalent most simplified Boolean representation for F is Z+XYZ