transitive relation

A relation R on a set A is transitive if for all a,b,c \in A, when aRb and bRc then aRc. Stated another way, whenever (a,b),(b,c) \in R then (a,c) \in R.

If there exists a, b, c \in R such that (a,b), (b,c) \in R but (a,c) \notin R then R is not transitive.

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