I have been getting a number of wrong solutions for this question. I am really stuck in this question. So kindly provide me with a logical solution to this question. Many Thanks in Advance.

Let S = {ab, bb} and let T = {ab, bb, bbb}.

(i) Show that S* T*, but that S* T*.

(ii) Prove in general that if S T then S* T*.

Find examples of S and T for which:

(iii) S T but S T and yet S* = T*. (iv) S* = T* but S T and T S. The symbol "" means "is not contained in or equal to."

Course Title: Theory of Automata. Topic: Formal Languages.