Logical Data Modeling - Binary Relation

1 - 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:

NHST try to find this relation.

3 - Properties

4 - 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 +

5 - Documentation / Reference


Data Science
Data Analysis
Statistics
Data Science
Linear Algebra Mathematics
Trigonometry

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