simplifying a boolean expression using DeMorgans

Question

This is the expression I need to simplify:

[{(AB)'*(BC)'} + (A'C)']'

Right now I have my answer as (AB + BC).(A' + C)

I don't think my answer is right but I'm not sure. IF someone could show steps on how to simplify that would be really appreciated, thanks!

Answer 1

((AB)'(BC)' + (A'C)')' = ((AB)'(BC)')'(A'C)''           ; DeMorgan
                       = ((AB)'' + (BC)'')(A'C)         ; DeMorgan + double negation
                       = (AB + BC)(A'C)                 ; double negation
                       = ABA'C + BCA'C                  ; distribution
                       = BCA'                           ; AA'=0