Universal quantification

In predicate logic, a 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 words, 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.2·0 = 0 + 0, and 2·1 = 1 + 1, and 2·2 = 2 + 2, etc.For all natural numbers n, 2·n = n + n.For all natural numbers n, 2·n > 2 + nFor all composite numbers n, 2·n > 2 + nFor all natural numbers n, if n is composite, then 2·n > 2 + n.For all natural numbers n, 2·n > 2 + n.For all natural numbers n, if n is composite, then 2·n > 2 + nFor all composite numbers n, 2·n > 2 + n.Given any living person x, that person is marriedIt is not the case that, given any living person x, that person is married In predicate logic, a 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 words, 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 only asserts that the property or relation holds for at least one member of the domain. Quantification in general is covered in the article on quantification (logic). Symbols are encoded .mw-parser-output .monospaced{font-family:monospace,monospace}U+2200 ∀ .mw-parser-output .smallcaps{font-variant:small-caps}FOR ALL (HTML ∀ · ∀ · as a mathematical symbol).