Simplifying a boolean algebra equation (A'B + AC + ABC' + BC)

Question

$A'B + AC + ABC' + BC$

$A'B+AC+ABC'$ (Complement's theorem)

Could I get a hint of where to proceed next? I've been going back and forth looking at theorems but can't understand how one would fit with all the different variables.

Answer 1

You can change the ABC' to AB because ABC is part of AC, like this:

$A'B + AC + ABC' + BC = A'B + AC + ABC' = A'B + ABC + AB'C + ABC' = A'B + ABC + AB'C + ABC + ABC' = A'B + AC + AB = B + AC$