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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}\$

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

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