Definition:Universal Statement

Definition
A universal statement is one which expresses the fact that all objects (in a particular universe of discourse) have a particular property.

That is, a statement of the form:
 * $\forall x: \map P x$

where:
 * $\forall$ is the universal quantifier
 * $P$ is a predicate symbol.

It means:
 * All $x$ (in some given universe of discourse) have the property $P$.

Note that if there exist no $x$ in this particular universe, $\forall x: \map P x$ is always true: see vacuous truth.

Also known as
A universal statement can also be referred to as a universal sentence, or more wordily, a sentence of a universal character.

Also see

 * Definition:Existential Statement


 * Definition:Bound Variable