How to simplify the Boolean expression (A'B+C)'(C+A)?

Question

I am trying to solve the following problem:

(A'B+C)'(C+A)

= (AB'+C')(C+A)

= AB'C+AB'A+C'C+C'A

= AB'C+AB'A+0+C'A

= AB'C+AB'+C'A

Than what?

Answer 1

You have applied De Morgan incorrectly in the first step... $$(A'B+C)'(C+A)=((A'B)'C')(C+A)$$ $$=(A+B')C'(C+A)=(A+B')C'A=AC'$$

Answer 2

$(A'B+C)' = (A'B)'C' = (A+B')C'$ to begin with.