I'm currently learning about boolean expressions. Currently, we're looking at how to simplify them. For this question I need to show the intermediate steps using the laws of boolean algebra.
However, I'm not sure where to start with this one (overline is negation):
$A\overline{B} + \overline{B}C + AB\overline{C}$
needs to be simplified to
$\overline{B}C + A\overline{C}$
Can anyone help me out? Thank you!
Best Answer
I will use $'$ for negation, it's just more convenient.
\begin{split}AB' + B'C + ABC' & = AB'(C'+C) + B'C + ABC'\\ & = AB'C' + AB'C + B'C + ABC' \\ & =AB'C' + ABC' + AB'C + B'C \quad (\text{rearranging terms}) \\ & = AC'(B'+B) + B'C(A+1) \\ & = AC' +B'C\end{split}