Universal: "For all x, P(x)" — true when P(x) is true for every x in the domain. Existential: "There exists x such that P(x)" — true when at least one x satisfies P(x). Negation swaps them: ~(for all x, P(x)) = there exists x, ~P(x). ~(there exists x, P(x)) = for all x, ~P(x). This quantifier interchange is frequently tested.