Universal quantifier

logical quantification stating that a statement holds for all objects
(Redirected from Given any)

In mathematics and logic, the universal quantifier is a quantifier used to state that a proposition applies to all elements in the universe of discourse. An example that uses this quantifier would be the proposition "All men are mortal". Usually, a turned A (∀) is used to denote the universal quantifier, "for all x" is written as either "∀x", "∀(x)".[1][2][3]

Predicate logic and syllogisms look at the properties of universal quantification.

Propositions can be falsified. To falsify a proposition which contains a universal quantifier, it is sufficient to find one element of the universe of discourse where the proposition is false. This element is known as a counterexample.



  1. "Comprehensive List of Logic Symbols". Math Vault. 2020-04-06. Retrieved 2020-09-04.
  2. "1.2 Quantifiers". www.whitman.edu. Retrieved 2020-09-04.
  3. "Predicates and Quantifiers". www.csm.ornl.gov. Retrieved 2020-09-04.