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Transitive Relation




In Mathematical Notation , this is:

: orall a, b, c \in X,\ a R b \and b R c \; \Rightarrow a R c


COUNTING TRANSITIVE RELATIONS


Unlike other relation properties, it is not possible to find a general formula that counts the number of transitive relations on a finite set. However, there is a formula for finding the number of relations which are simultaneously ''reflexive, symmetric,'' and ''transitive''


EXAMPLES


For example, "is greater than" and "is equal to" are transitive relations: if ''a'' = ''b'' and ''b'' = ''c'', then ''a'' = ''c''.

On the other hand, "is the mother of" is not a transitive relation, because if Alice is the mother of Brenda, and Brenda is the mother of Claire, then Alice is not the mother of Claire.

Examples of transitive relations include:


OTHER PROPERTIES THAT REQUIRE TRANSITIVITY



SEE ALSO



EXTERNAL LINKS




SOURCES

  • Discrete and Combinatorial Mathematics - Fifth Edition - by Ralph P. Grimaldi