Main Page | See live article | Alphabetical index 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. This article is from Wikipedia. All text is available under the terms of the GNU Free Documentation License.