Transitive closure
= Transitive closure
{title2=$\operatorname{TC}(x)$}
The transitive closure $\operatorname{TC}(x)$ is the least transitive set containing every member of $x$. It is obtained by taking the union of all finite iterates of the union operation starting from $x$. This set-theoretic construction uses the membership <binary relation>; <transitive closure of a relation> instead closes an arbitrary <binary relation> under composition.