This question is listed in my textbook:
Give an example of a Boolean algebra B and elements $x$, $y$, $z$ in $B$ such that $x + z = y + z$, but $x \neq y$.
Now, I believe this means I have to use the axioms of Boolean algebra to prove that expression, correct? I managed to simplify it like so: $$ x + z + (y'z') = 1 = x + (z + y')(z + z') = x + y' + z $$ I'm not sure if that was what I was supposed to do, but using that I was able to find three conditions where $x + z = y + z$, but $x \neq y$ is true.