Simplifying a Boolean expression (confused)

Question

Could somebody help me make sense of how to use the Boolean rules to simplify this expression? $$(x'+(yz)')(x + z')'$$ I used distributivity to get $$(x'+y')(x'+z')(x'+z)$$ I don't know if that was the right path to go down, or where to go from here. Thanks.

Answer 1

I'd rather take this from the start: $$(x'+(yz)')(x+z')'$$ Apply De Morgan's laws to $(yz)'$ and $(x+z')'$: $$=(x'+y'+z')zx'$$ Distribute: $$=zx'x'+zx'y'+zxz'$$ $x'x'=x'$ and $zz'=0$: $$=zx'+zx'y'$$ $zx'$ absorbs $zx'y'$: $$=zx'$$ This is the simplest form.