Simplification of a logic equation

Question

I am trying to simplify this logic function: $$g(x,y,z)=xy+x'z+yz$$ without Carnot (just Boole algebra). I tried going like this $$(x\cup y)\cap(x'\cup y)\cap(z\cup y)$$ and then using the distributive property of sets but it leads nowhere. Thanks in advance

Answer 1

$$g(x,y,z)=xy+x'z+yz $$ Last term $yz$ has a common variable with the first two terms. This suggests to combine it with the first two as: $$\begin{align}g(x,y,z)&=xy+x'z+\color{blue}{yz}\\ &= xy+x'z+\color{blue}{yz(x+x')}\\ &=xy+\color{blue}{xyz} + x'z + \color{blue}{x'yz}\\ &=xy(1+z)+x'z(1+y)\\ &=xy+x'z \end{align}$$

Because $x+x'=1$ and $1+z=1$