Transitivity

In mathematics, transitivity is a mathematical property of binary relations such that if A and B are related, and B and C are related, then it follows that A and C are also related, for all A, B, and C for which the relation may apply. The relation is then said to be transitive.

In 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.

Example of transitive relations include:

• "is equal to" -- equality
• "is a subset of"

If a transitive relation is also reflexive and symmetric, then it is said to be an equivalence relation.

See also Transitive closure.