# Data Modeling - Binary Relation

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 +