# How to simplify this using boolean algebra?

My paper is due tomorrow and there is only the last exercise left for me to do. However, I don't have any sufficient notes or examples on how to simplify it. Any help would be appreciated!

A'B'C' + A'B'C + ABC'

• Hints: $XY \lor XY' = X(Y \lor Y') = X\land 1 = X$ Dec 3 '13 at 19:30

We use the distributive law (DL), and the identities $$P + P' = 1\tag{1}$$ $$1\cdot P = P\cdot 1 = P\tag{2}$$
\begin{align} \color{blue}{\bf A'B'}C' + \color{blue}{\bf A'B'}C + ABC' &= \color{blue}{\bf A'B'}(C + C') + ABC' \tag{DL} \\ \\ & = A'B'(1) + ABC'\tag{1} \\ \\ & = A'B' + ABC' \tag{2}\end{align}
$\bar{A}\bar{B}\bar{C}+\bar{A}\bar{B}{C}+{A}{B}\bar{C}=(\bar{A}\bar{B}\bar{C}+\bar{A}\bar{B}{C})+{A}{B}\bar{C}=\bar{A}\bar{B}(\bar{C}+C)+{A}{B}\bar{C}=\bar{A}\bar{B}+{A}{B}\bar{C}$