Question

Given F (x, y, z) = (x’ + z) (x’ + y’)’ (y’ + z’) write the expression for the dual of F and complement of F.

Answer 1

Given F (x, y, z) = (x’ + z) (x’ + y’)’ (y’ + z’)

F (x, y, z) = (x’ + z) [(x’)' (y’)’] (y’ + z’) { We know that (P+Q)'= P' Q' }

F (x, y, z) = (x’ + z) (xy) (y’ + z’) { We know that (P')'= P }

F (x, y, z) = (x’ + z) (xy) (y’ + z’)

Dual Defintiion: Dual of a function is Nothing but Interchanging addition and Multiplication in the given Function

From the above the Dual of F is

F_Dual (x, y, z) = (x’z) + (x + y) + (y’z’)

Complement of Funtion:

Definition: Find the Dual of the given Function and then Invert the each Boolean Variable in the Dual Function

Given Dual Function is

F_Dual (x, y, z) = (x’z) + (x + y) + (y’z’)

Complement of above Function is

F'(x, y, z) = (x+z') + (x' + y') + (y+z)