Complement of a Function (1.9)

•  The complement of a function is obtained by interchanging AND and OR operations and complementing each variable and constant.
• Or change 1s to 0s and 0s to 1s in the truth table column containing F’s value.
• One should not confuse the complement of a function with the dual of a function.

Example:   Find G(x,y,z), the complement of  F(x,y,z) = x’yz’ + x’y’z

                                                                                                                                                     G = F’ = (x’yz’ + x’y’z)’= (x’yz’)’•(x’y’z)’= (x+y’+z)•(x+y+z’)

                           Find  H(x,y,z), the dual of F(x,y,z) = x’yz’ + x’y’z

                                                                                                                                                                                                                                                                                        H  = (x’+y+z’) (x’+y’+ z)