In mathematics, a binary relation R over a set X is transitive if whenever an element a is related to an element b, and b is in turn related to an element c, then a is also related to c. Transitivity is a key property of both partial order relations and equivalence relations.
== Formal definition ==
In terms of set theory, the transitive relation can be defined as:
∀
a
,
b
,
c
∈
X
:
(
a
R
b
∧
b
R
c
)
⇒
a
R
...