Predicates enable an abstraction over Propositions so expressions may be formed that apply to a variable, rather than a concrete statement. They behave as functions that return either \(true\) or \(false\), depending on their variable(s). When all variables are bound to given values, predicates become propositions.


Symbol Term Description
\(\forall\) universal \(\forall x\ P(x)\) symbolises the predicate \(P(x)\) is true for every value in the universe of discourse
\(\exists\) existential \(\exists x\ P(x)\) the predicate \(P\) holds for at least one \(x\)
\(\exists!\) uniqueness \(\exists! x\ P(x)\) expresses there exists a unique value \(x\) for which \(P(x)\) is true

Note: the precedence of quantifiers takes higher priority than any predicate connectives.