## 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

- is a subset of (set inclusion, a relation on sets)

## Key Property

Transitivity is a key property of both:

## Rule

A transitive relation is:

- if and only if it is irreflexive

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