Logical Data Modeling - Transitive Relationship Property
Table of Contents
1 - About
transitive is a relationship property that tells that the relationship follows the following rule:
- when the relation relates a to b and b to c, then the relation relates a to c.
In mathematical notation, the relation f is transitive between x and y and z when <MATH> y = f(x) \\ z = f(y) \\ \text{then } z = f(c) \\ </MATH>
2 - Articles Related
3 - Example
- Transitive example: is an ancestor of : if Amy is an ancestor of Becky, and Becky is an ancestor of Carrie, then Amy is an ancestor of Carrie.
- Non Transitive example: is the birth parent of: if Alice is the birth parent of Brenda, and Brenda is the birth parent of Claire, then Alice is not the birth parent of Claire.
4 - List
- ancestor
- is a subset of (set inclusion, a relation on sets)
- divides (divisibility)
5 - Key Property
Transitivity is a key property of both:
6 - Rule
A transitive relation is:
- if and only if it is irreflexive
if aRb and bRa, transitivity gives aRa, contradicting irreflexivity.