Negation of Formal Logic

Question

What domain is U and what is P(x) in order for this statement to be false?

∀x∈U, P(x) ⇒ ∃x∈U, P(x) 

I don't think this is possible but I am hoping someone can figure out how to make this statement false.

Answer 1

I'd imagine that if U is the empty set, that statement is false; there does not exist any element in U, not least one that satisfies P(x). The antecedent is a vacuous truth, but is nevertheless still true.