In mathematics, the transitive closure of a binary relation R on a set X is the smallest relation on X that contains R and is transitive. 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: "it is possible to fly from z to w in one or more flights for any z and w in X." Informally, the transitive closure is the set of all places you can get to from any starting place.