2. Can there exist two sets A and B so that both A B and A B? Either provide an example of such sets, or else explain why this cannot happen.

3. The power set of a set S is defined to the the set consisting of all subsets of S. For example, the powers et of {a} is {, {a}}. (a) Determine the power sets of {a, b} and of {a, b, c}. (b) Is there a set P such that the power set of P has exactly one element? Justify your answer.