Let R be a relation on the set A. Define Tr = {(x,y) element of AxA | for some natural number n, there exist a0=x, a1, a2, ..., an = y element of A such that (a0, a1), (a1, a2),..., (an-1, an) element of R}.

Prove that R is transitive. (Tr is the transitive closure of R.)

I really don't know how to prove this. I know that if it is transitive, (a,b), (b,c) element of Tr --> (a,c) element of Tr. Then what?