Data Modeling - Binary Relation

1 - About

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 +

4 - Documentation / Reference

data/modeling/binary_relation.txt · Last modified: 2017/09/13 21:21 by gerardnico