Two languages such that their Kleene closures are equal I am trying to solve the following problem:
Find languages S and T over the alphabet $\{a, b\}$ such that $ S \not\subset T $ and $ T \not\subset\ S $ ($S$ is not contained in $T$ and not equal to $T$, $T$ is not contained in $S$ and is not equal to $S$) but $S^* = T^*$.
It might be trivial, but I would appreciate some help.
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.