I am trying to understand the simplification of the boolean expression:
AB’ + BC + C’A
I know it simplifies to
A + BC
And I understand why, but I cannot figure out how to perform the simplification through the expression using the boolean algebra identities. I was wondering if someone could show me the steps needed to do this. Thank you in advance.
You can use absorption to say $B'=B'+B'C$ so
$$B'+BC+C' = B'+B'C+BC+C'=B'+(B'+B)C+C'= B'+C+C'=B'+1=1$$ and so $$AB'+ABC+AC' = A(B'+BC+C')=A$$
You can use absorption again to say $BC=BC+ABC$ so $$AB' +BC + AC' = AB' +BC + ABC+ AC' = A(B'+BC+C')+BC=A+BC$$