Q:

find a universe for variables x, y, and z for which this statement is true and another universe in which it is false

Im solving a practice quesitons on quantifiers and I'm stuck with this questions
im trying to solve this question for few hours now and I really don't have a clue what to do...
The question is 

Find a universe for variables $x$, $y$, and $z$ for which the statement 
  $$\forall x∀y((x\ne y) → ∀z((z = x) ∨ (z = y)))$$
  is true and another universe in which it is false

Detailed explanation will be really much appreciated.
Thanks in advance guys!

A:

Hint: The logical negation of
$$ x\ne y\to (z=x\lor z=y)$$
is
$$x\ne y \land z\ne x\land z\ne y$$
or
$$x,y,z\text{ are three distinct objects}$$

