# Simplify Boolean expression

The following Boolean expression is simplified into its minimal number of literals:

$$x'y' + yz +x'yz' \implies x'+yz.$$

How do you logically conclude this using the Boolean Laws?

• Please don't delete your question after receiving an answer. Thank you! – D.W. Apr 3 at 22:30

\begin{align*} x'y' + yz + x'yz' &= x'y' (z+z') + (x+x')yz +x'yz' &\mbox{(identity)} \\&= x' y' z + x' y' z' + xyz + x'yz + x'yz' &\mbox{(distributivity)} \\&= x' y' z + x' y' z' + xyz + x'yz + x'yz + x'yz' &\mbox{(idempotence)} \\&= x'(y' z + y' z' + y z + y z') + (x+x')yz &\mbox{(distributivity)} \\&= x'+yz. &\mbox{(identity)} \end{align*}