Full Idea
A relation is 'transitive' on a set if the relation can be carried over from two ordered pairs to a third.
Gist of Idea
A relation is 'transitive' if it can be carried over from two ordered pairs to a third
Source
Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0)
Book Reference
Enderton,Herbert B.: 'A Mathematical Introduction to Logic' [Academic Press 2001], p.5