We will show that the reflexive closure of a transitive closure of a relation is equal to the transitive closure of its reflexive closure through a series of simpler results: [3 marks] let ribe a transitive relation on a set s, show that its reflexive closure rr is also transitive. [3 marks] let rą be a reflexive relation on a set s, show that its transitive closure tr, is also reflexive. [3 marks] using the previous results or otherwise, show that r(tr) = t(rr) for any relation r on a set. hint: you may find the fact that transitive (resp. reflexive) closures of r are the smallest transitive (resp. reflexive) relation containing r useful.