# Data Modeling - Binary Relation

### Table of Contents

## 1 - About

Binary Relation is a relation between two elements.

Binary relations are used in many branches of mathematics to model concepts like:

- order relation such as “is greater than”, “is equal to”, and “divides” in arithmetic,
- “is congruent to” in geometry,
- “is adjacent to” in graph theory,
- “is orthogonal to” in linear algebra
- and many more.

The concept of function is defined as a special kind of binary relation.

## 2 - Articles Related

## 3 - Example

Example: Suppose there are:

- four objects
`ball, car, doll, gun`

- four persons
`John, Mary, Ian, Venus`

The `owns`

binary relation between the objects and the persons is:

`John`

owns the`ball`

,`Mary`

owns the`doll`

,`Venus`

owns the`car`

,`Nobody`

owns the`gun`

,`Ian`

owns`nothing`

.

This relation may be represented:

R = ( {ball, car, doll, gun}, {John, Mary, Ian, Venus}, { (ball, John), (doll, Mary), (car, Venus) } )

ball | car | doll | gun | |
---|---|---|---|---|

John | + | |||

Mary | + | |||

Ian | ||||

Venus | + |

Two different relations could have the same graph. The graphs of the relations above and below are the same.

R = ( {ball, car, doll, gun}, {John, Mary, Venus}, { (ball, John), (doll, Mary), (car, Venus) } )

ball | car | doll | gun | |
---|---|---|---|---|

John | + | |||

Mary | + | |||

Venus | + |