3 ms·

Read up on DeMorgan’s law.

• thaumasiotes 7y ago
  De Morgan's law isn't the right one for this. You want the identity ∀x.P(x) ⟺ ¬∃x.¬P(x). ∀x.P(x) is obviously true when the universe is empty -- no counterexamples exist. ∃x.P(x) is obviously not true in that case -- no examples exist.
  • deleted 7y ago
    [deleted]
  • maweki 7y ago
    That is De Morgan if you expand the quantifiers.
    • thaumasiotes 7y ago
      You have to make some assumptions if you want to "expand the quantifiers". In particular, you have to assume that the universe is non-empty, which is a really bad idea if you're commenting in this thread.