Question

Find a universe for variables xyz and w for which the statement ∀x∀y∀z∃w((w≠x)^(w≠y)^(w≠z)) is ture and another universe in which it is false.

Answer 1

For the false one I said universe: all variable consist of value 1 which makes the statement false? I don't know how to show if it's true would I go like universe: all variable w =0 and all other variables are non zero?

Answer 2

I posted this earlier but didn't get any replies any ideas would be greatly appreciated!