Universal+Quantification

Universal quantification
In [|predicate logic], an universal quantification is a type of [|quantifier], a [|logical constant] which is [|interpreted] as "given any" or __**"for all."**__ It expresses that a [|propositional function] can be [|satisfied] by every [|member] of a [|domain of discourse]. In other terms, it is the [|predication] of a [|property] or [|relation] to every member of the domain. It [|asserts] that a predicate within the [|scope] of a universal quantifier is true of every [|value] of a [|predicate variable].

It is usually denoted by the [|turned A] (∀) [|logical operator] [|symbol], which, when used together with a predicate variable, is called a **universal quantifier** ("∀x", "∀(x)", or sometimes by "(x)" alone). Universal quantification is distinct from [|//existential// quantification] ("there exists"), which asserts that the property or relation holds only for at least one member of the domain. Quantification in general is covered in the article on [|quantification]. Symbols are encoded [|U+]2200 ∀ for all (HTML: ∀ &forall; as a mathematical symbol).