Simplifying Boolean Expression x'yz + xy'z + xyz' + xyz

Question

Hi I'v solved this halfway, please help me for the rest.
so far I've got..

    x'yz + xy'z + xyz' + xyz
    z(x'y + xy') + xy(z'+z)
    z(x'y + xy') + xy

i don't understand how to solve the z(x'y + xy') part of this expression.. please somebody help..

Answer 1

x'y + xy' is XOR. So you can simplify to z(x+y) + xy because z(x'y + xy') + xy is z when x != y and xy when x == y.

The (x+y) after z is necessary to disallow influence of z when x == y == 0.