Hi, this is a pretty noob-ish question but I'm having some difficulty grasping this.

I have a function f(x,y,z)

I've gotten it down to this:
f(x,y,z) = x'y + xz

I'm thinking that the final answer should be y + z but I don't know how to prove it.
My thoughts go like this, if you set x=0 then you'll get y and if you set x=1 you should still get z, but I can't seem to prove it.

Am I going about this the right way?

 

You can't simplify it anymore. A Karnaugh map will show it to you.

An example: set x=0, y=0 and z=1
x'y+xz=0
but y+z=1

 

This is a relatively simple (small) function. It would be easy to prove whether or not your thinking is correct by making a truth table for each function (one for x'y + xz and one for y+z) then compare the results. If they produce the same output, then you can go from there, but I think you'll find that is not the case...