Question

(4) Find a common domain for the variables x, y, and z for which the statement
∀x∀y((x=/=y) => ∀z((z=x)v(z=y)))
is true and another domain for which it is false.

Answer 1

It is true on every set with no more than $2$ members and false on other sets.

For example, it is true on $\{a,b\}$ and false on $\mathbb R$