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:

• order relation such as greater than, is equal to, and divides in arithmetic
• is part of in taxonomy
• is congruent to in geometry,
• is adjacent to in graph theory,
• is orthogonal to in linear algebra
• is equal to
• and many more.

NHST try to find this relation.

Articles Related

Properties

• Logical Data Modeling - Asymmetric Relation (Uni-directional|Antisymmetric)
• Logical Data Modeling - Antisymmetry relationship
• Logical Data Modeling - Symmetric relationship (bi-directional)
• Logical Data Modeling - Reflexive relationship property
• Logical Data Modeling - Transitive Relationship Property

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)
     }
)

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)
    }
)

Documentation / Reference

• wiki/binary_relation