Two languages such that their Kleene closures are equal
I had originally assumed that the sets are disjoint, but there's no such requirement in the question. I'll post my solution in case anyone might have the same problem in future.
S = {a, b, ab}
T = {a, b, ba}
S* = T* since the intersection has all the letters of the alphabet plus ab and ba can easily be obtained from a and b.