Simplify Boolean expression
$$
\begin{align*}
x'y' + yz + x'yz' &amp;=
x'y' (z+z') + (x+x')yz +x'yz' &amp;\mbox{(identity)} \\&amp;=
x' y' z  + x' y' z' + xyz + x'yz + x'yz' &amp;\mbox{(distributivity)} \\&amp;=
x' y' z  + x' y' z' + xyz + x'yz + x'yz  + x'yz' &amp;\mbox{(idempotence)} \\&amp;=
x'(y' z + y' z' + y z + y z') + (x+x')yz &amp;\mbox{(distributivity)} \\&amp;=
x'+yz. &amp;\mbox{(identity)}
\end{align*}
$$