High Quality Content by WIKIPEDIA articles! In mathematics, the
transitive closure of a binary relation R on a set X is the
smallest transitive relation on X that contains R (Lidl and Pilz
1998:337). If the original relation is transitive, the transitive
closure will be that same relation; otherwise, the transitive
closure will be 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
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