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:
Subsets are transitive: if A is a subset of B and B is a subset of C, then A is a subset of C.
Height is transitive: if Sidney is taller than Casey, and Casey is taller than Jordan, then Sidney is taller than Jordan.
Rock, paper, scissors is not transitive: rock beats scissors, and scissors beats paper, but rock doesn't beat paper. This is called an intransitive relation.
Given a relation , the smallest transitive relation containing is called the transitive closure of , and is written as .[2]