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>

Articles Related

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.

List

• ancestor
• Is greater than,
• Is less than,
• is equal to (equality)
• is a subset of (set inclusion, a relation on sets)
• divides (divisibility)
• is dependent of

Key Property

Transitivity is a key property of both:

• partial orders
• equivalence relations

Rule

A transitive relation is:

• asymmetric
• if and only if it is irreflexive

if aRb and bRa, transitivity gives aRa, contradicting irreflexivity.

Documentation / Reference

• wiki/Transitive_relation