# Simplify using Boolean Algebra

I can simplify this using Kmaps, but can't figure out how to using boolean algebra. If anyone could show me the steps I'd really appreciate it.

$F = \bar{x}\bar{y}\bar{z} + xy + x\bar{z}$

should simplify to:

$F= xy + y\bar{z}$

• sorry, fixed with edit – Austin May 6 '15 at 19:49
• The site supports mathjax so I added it to your equations. – Dean May 6 '15 at 19:56

Use the identities: $a+\bar{a} = 1$ and $a+1 = 1$

$\bar{x}\bar{y}\bar{z}+x\bar{z}+xy$

$\bar{x}\bar{y}\bar{z}+x\bar{z}(y+\bar{y})+xy$

$\bar{x}\bar{y}\bar{z}+x\bar{z}y+x\bar{z}\bar{y}+xy$

$\bar{x}\bar{y}\bar{z}+x\bar{z}\bar{y}+x\bar{z}y+xy$

$(\bar{x}+x)\bar{y}\bar{z}+(\bar{z}+1)xy$

$\bar{y}\bar{z}+xy$