For any relation R, the transitive closure of R always exists.

This relation R can be visualized as follows:

For example, consider the relation R as "equal to and odd".

A binary relation R on a set X defines a directed graph.

The relation R (table) is in second normal form (2NF)

Examples 2.3.6 (i) The relation R defined on the plane by setting is an e.r.

The following set is the set of pairs for which the relation R holds.

There are mainly two approaches to store a relation r in a distributed database system:

The relations are given as a (finite) binary relation R on Σ.

In the typical situation, the relation R is simply given as a set of equations, so that .