Final answer:
The sets S* = {ab, bb}* and T* = {ab, bb, bbbb}* are equal because any string that can be formed from T can also be formed from S through concatenation, and vice versa, as S is a subset of T.
Step-by-step explanation:
To prove that S* = T*, we must first understand the concept of a Kleene star. For any set of strings, the Kleene star operation allows us to generate all possible strings, including the empty string, by concatenating zero or more strings from the original set. In this particular problem, the sets are S = {ab, bb} and T = {ab, bb, bbbb}.
Notice that the string 'bbbb' can be generated by concatenating 'bb' from set S twice, i.e., 'bb' + 'bb'. Because of this, every string that can be formed from T can also be formed from S by using concatenation. Similarly, since the elements of S are also elements of T, any string generated by S* can also be formed by T*. Thus, it can be concluded that S* and T* generate the same set of strings, proving that S* = T*.