- #1
Danijel
- 43
- 1
So, here's my question. I read somewhere that all universal truths on empty domains are vacuously true, whereas all existential are false. However, if all statements of the form (∀x∈A)(P(x)) , where A is an empty set, are vacuously true, then the statement (∃x∈A)(P(x)) should also be true, because if something holds for all x, then there obviously exists an x for which the statement holds (in fact, it holds for every x). Am I wrong?