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)".
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.