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.

In notation, this is:

$aRb\wedge bRc\Rightarrow aRc$

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.

See also Transitive closure.