# Universal quantification

## Logical quantification stating that a statement holds for all objects / From Wikipedia, the free encyclopedia

#### Dear Wikiwand AI, let's keep it short, summarize this topic like I'm... Ten years old or a College student

In mathematical 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 predicate 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.

**Quick facts: Type, Field, Statement, Symbolic statement...**▼

Type | Quantifier |
---|---|

Field | Mathematical logic |

Statement | is true when is true for all values of . |

Symbolic statement |

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). The universal quantifier is encoded as U+2200 ∀ FOR ALL in Unicode, and as `\forall`

in LaTeX and related formula editors.