Editing Negation (section)

=== Negations of quantifiers ===
In [[first-order logic]], there are two quantifiers, one is the universal quantifier <math>\forall</math> (means "for all") and the other is the existential quantifier <math>\exists</math> (means "there exists"). The negation of one quantifier is the other quantifier (<math>\neg \forall xP(x)\equiv\exists x\neg P(x)</math> and <math>\neg \exists xP(x)\equiv\forall x\neg P(x)</math>). For example, with the predicate ''P'' as "''x'' is mortal" and the domain of x as the collection of all humans, <math>\forall xP(x)</math> means "a person x in all humans is mortal" or "all humans are mortal". The negation of it is <math>\neg \forall xP(x)\equiv\exists x\neg P(x)</math>, meaning "there exists a person ''x'' in all humans who is not mortal", or "there exists someone who lives forever".