Finitary relation

In mathematics, a finitary relation is a property that assigns truth values to finite tuples of elements. Typically, the property describes a possible connection between the components of a k-tuple. For a given set of k-tuples, a truth value is assigned to each k-tuple according to whether the property does or does not hold. When k = 2, one has the most common version, a binary relation.When two objects, qualities, classes, or attributes, viewed together by the mind, are seen under some connexion, that connexion is called a relation. In mathematics, a finitary relation is a property that assigns truth values to finite tuples of elements. Typically, the property describes a possible connection between the components of a k-tuple. For a given set of k-tuples, a truth value is assigned to each k-tuple according to whether the property does or does not hold. When k = 2, one has the most common version, a binary relation. 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: Each row of the table records a fact or makes an assertion of the form 'X thinks that Y likes Z '. For instance, the first row says, in effect, 'Alice thinks that Bob likes Denise'. The table represents a relation S over the set P of people under discussion: