# Logical Data Modeling - Transitive Relationship Property

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 $$y = f(x) \\ z = f(y) \\ \text{then } z = f(c) \\$$

## 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.

## Key Property

Transitivity is a key property of both:

## Rule

A transitive relation is:

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

## Documentation / Reference

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