Hello everyone. I have a proof that I am having trouble beginning. Should try to solve this proof directly or by induction?

Thanks.

ProveLet R be a binary relation on a set A, and let R

^{T}be the transitive closure of R . Prove that for all x and y in A, (x,y) ∈ R^{T }if and only if there is a sequence of elements of A say x_{1, }x_{2},…x_{n}, such that x = x_{1}, x_{1}Rx_{2}, x_{2}Rx_{3}, …, x_{n-1}Rx_{n}= y