I am trying to understand the simplification of the boolean expression:
AB + A'C + BC
I know it simplifies to
A'C + 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.
Best Answer
\begin{align*} &\mathrel{\phantom{=}}AB+A'C+BC\\ &=AB+A'C+BC(A+A') \quad \text{($A+A'=1$, Complementarity law)}\\ &=AB+A'C+ABC+A'BC\\ &=AB+ABC+A'C+ABC \quad \text{(Associative law)}\\ &=AB+A'C \quad \text{(Absorption law)} \end{align*}