Quantifiers

Quantifiers are words, expressions, or phrases that indicate the number of elements that a statement pertains to. In mathematical logic, there are two quantifiers: the universal quantifier ("for all") and the existential quantifier ("there exists").

Universal quantifier: This quantifier is used to state a proposition that is true for all variables x of a given set. For example, the proposition "x^2 is a nonnegative number" is true for every real number, so we state "for all real numbers $x$, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x^2 } is nonnegative". Symbolically, we write the universal quantifier as $\forall$ (for example, $\forall x\in \mathbb {R} ,x^{2}\geq 0$).

Universal quantifier: This quantifier is used to state a proposition that is at least true for one element x of a given set. For example, the proposition "n is greater than 7" is not true for all real numbers, but we know it is true for some.

Resources

• Quantifiers, Mathematics LibreTexts