# Data Modeling - Binary Relation

relationship in Binary.

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.

## 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 +