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

Question

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!

Answer 1

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 $$x,y,z\text{ are three distinct objects}$$

Answer 2

Hint: Try $U = \emptyset, U=\{1\}, U=\{1,2\}$ and $U=\{1,2,3\}$