does ∀xP(x) imply∃xP(x)?
Got asked this question on an exam, I'm not entirely sure what is being asked here. Though I'd put it out there, maybe somebody knows and could explain.
I answered yes, thinking that if ∀xP(x) is true then ∃xP(x) has to be true as well, while if ∀xP(x) is false then ∃xP(x) may or may not be true which would make ∀x →∃x true in every possible scenario. Honestly I don't think I even understand the question, is this even a valid question?