Boolean Simplification $ABC' + BC'D' + BC + C'D$

Question

I'd like to simplify this equation: $ABC' + BC'D' + BC + C'D$ prove it to $B + C'D$

My attempt is : $$\begin{align} &= ABC' + BC'D'(A+A') + BC + C'D\\ &= ABC' + ABC'D' + A'BC'D' + BC + C'D\\ &= ABC'(1 + D') + A'BC'D' + BC + C'D\\ &= ABC' + A'BC'D' + BC + C'D\end{align}$$

and then i'm running out of idea.. can anyone help me what i suppose to do next step? Thank you

Answer 1

ok here is solution algebraically( although i still insist Karnaugh Map is much more simple for the 4 variable case): $$ABC' + BC'D' + BC + C'D = ABC' + BC'D' + BC + C'D(1+B)=ABC' + BC'D' + BC + C'D+BC'D = B(AC'+C'D'+C+C'D)+C'D=B(AC'+C+C'(D'+D))+C'D=B(AC'+C+C')+C'D=B(AC'+1)+C'D=B+C'D$$