In mathematical notation, this is:
For example, "is greater than" and "is equal to" are transitive relations: if a = b and b = c, then a = c.
On the other hand, "is the mother of" is not a transitive relation, because if Alice is the mother of Brenda, and Brenda is the mother of Claire, then Alice is not the mother of Claire.
Examples of transitive relations include:
- "is equal to" (equality)
- "is a subset of" (set inclusion)
- "is less than" and "is less than or equal to" (inequality)
- "divides" (divisibility)