# Logical Data Modeling - Binary Relation

A binary relation is a relationship between two elements that is implemented via a binary function.

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

NHST try to find this relation.

## 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 +