In more concrete terms the transitive closure of R is the relation R* such that xR*y if xRy, or if xRz for some z with zRy, or if xRz and zRw and wRy for some z and w in X, and so on for any number of intermediates. If X is the set of humans (alive or dead) and R is the relation 'parent of', then xR*y means y is a direct descendant of x.

- If
*xRy*means*x*is the parent of*y*, then the transitive closure of*R*is the relation "*x*is an ancestor of*y*." - If
*xRy*means "there is a regular direct airplane flight from airport*x*to airport*y*", then the transitive closure of*R*is the relation "it is possible to fly from*x*to*y*in one or more flights."