Transitivity (mathematics)

In logic and mathematics, transitivity is a property of a binary relation. It is a prerequisite of a equivalence relation and of a partial order.
Definition and examples.
In general, given a set with a relation, the relation is transitive if whenever a is related to b and b is related to c, then a is related to c. For example:
Given a relation formula_1, the smallest transitive relation containing formula_1 is called the transitive closure of formula_1, and is written as formula_4.