I am trying to simplify x’y’z’ + x’yz + xy’z’ + xy’z + xyz

from using online calculators, i think the sum of products answer should be y’z’ + yz + xy'

but I am only getting as far as here:

= x’y’z’ + x’yz + xy’z’ + xy’z + xyz

= y’z’(x’ + x) + yz(x’ + x) + xy’z

= y’z’ + yz + xy’z

What basic Boolean rule says that I can take off that z?

And why can't I do something like

= y'z' + z(y + xy')

= y'(z'+z)(y + xy')

= oh man... i have been looking at this for hours

Can someone explain this to me?

- Dave