How to simplify the Boolean expression $A'BC + AB'C' + A'B'C' + AB'C + AB$?

Question

How to simplify this Boolean expression? $$A'BC + AB'C' + A'B'C' + AB'C + AB$$

I have solved it using Kmap and found the answer to be $$A + BC + B'C'$$

I tried simplifying it using the rules but only got to $$B'C' + C (A'B + AB') + AB$$

Seeing that I already have $B'C'$ in my answer, I assume I only need to simplify $C (A'B + AB') + AB$ to $A + BC$, but I don't know how.

I hope you can help me.

Answer 1

Write $AB=ABC+ABC’$ and go from there.

Answer 2

\begin{align}A'BC+AB'C'+A'B'C'+AB'C+AB&=A'(BC+B'C')+A(B'C'+B'C+B)\\ &=A'(BC+B'C')+A(B'(C'+C)+B)\\ &=A'(BC+B'C')+A(B'+B)\\ &=A'(BC+B'C')+A(1)\\ &=A'(BC+B'C')+A(1+BC+B'C')\\ &=A'(BC+B'C')+A+A(BC+B'C')\\ &=(A'+A)(BC+B'C')+A\\ &=A+BC+B'C'\\ \end{align}