# Logical Data Modeling - Binary Relation

### Table of Contents

## About

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:

- is part of in taxonomy
- is congruent to in geometry,
- is adjacent to in graph theory,
- is orthogonal to in linear algebra
- and many more.

NHST try to find this relation.

## Articles Related

## Properties

## 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 | + |