In mathematics, a finitary relation has a finite number of "places". In set theory and logic, a relation is a property that assigns truth values to -tuples of individuals. Typically, the property describes a possible connection between the components of a -tuple. For a given set of -tuples, a truth value is assigned to each -tuple according to whether the property does or does not hold.

An example of a ternary relation (i.e., between three individuals) is: " was introduced to by ", where is a 3-tuple of persons; for example, "Beatrice Wood was introduced to Henri-Pierre Roché by Marcel Duchamp" is true, while "Karl Marx was introduced to Friedrich Engels by Queen Victoria" is false.

Informal introduction

Relation is formally defined in the next section. In this section we introduce the concept of a relation with a familiar everyday example. Consider the relation involving three roles that people might play, expressed in a statement of the form "X thinks that Y likes Z ". The facts of a concrete situation could be organized in a table like the following: