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.