Prelude to Relationship: Relation ---- a well-known mathematical concept

OK, we have covered the E (Entity) in the ER-model
Next up: the R (Relationship) in the ER-model

Cartesian product:

Given two sets:
- A = {a₁, a₁, ..., a_m}
- B = {b₁, b₁, ..., b_n}
The cartesian product A × B of the sets A = {a₁, a₂, ..., , a_m} and B = {b₁, b₂, ..., , b_n} is:

Example:

A = {a, b, c} B = {3, 7} A × B = { (a,3), (a,7), (b,3), (b,7), (c,3), (c,7) }

Relation:

Example 1:

Given the sets:
An example of a relation between Students and Courses is:

Example 2:

Given the sets:
An example of a relation between Students and Majors is:

Higher degree relations

Higher degree cartesian products:

The cartesian product of 3 sets A, B and C is:

Example:

A = {a, b} B = {x, y} C = {1, 4} A × B × C = { (a,x,1), (a,x,2), (a,y,1), (a,y,2), (b,x,1), (b,x,2), (b,y,1), (b,y,2) }

Higher degree relations:

Given 3 sets:
- A = {a₁, a₁, ..., a_m}
- B = {b₁, b₁, ..., b_n}
- C = {c₁, c₁, ..., c_k}
A relation R between the 3 sets A, B and C is:

Nomenclature
- Types of relations:
- Notes:
Some notes on "Relation"
- The "relation" concept in Mathematics is static
  In other words:
  This is the main reason why a relation is not used in ER modeling (content of relations must change in database, e.g., more kids are born to parents)...
  Instead, ER-modeling uses the concept of relationship
- Nevertheless, but the relationship concept used in ER model is very closely related with the mathematical concept of relation