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.
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.
Solution
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