In mathematics, the **transitive closure** of a binary relation *R* on a set *X* is the transitive relation *R*+ on set *X* such that *R*+ contains *R* and *R*+ is minimal (Lidl and Pilz 1998:337). If the binary relation itself is transitive, then the transitive closure is that same binary relation; otherwise, the transitive closure is a different relation. For example, if *X* is a set of airports and *x R y* means "there is a direct flight from airport *x* to airport *y*", then the transitive closure of *R* on *X* is the relation *R*+: "it is possible to fly from *x* to *y* in one or more flights."

Read more about Transitive Closure: Transitive Relations and Examples, Existence and Description, Properties, In Graph Theory, In Logic and Computational Complexity, In Database Query Languages, Algorithms

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