Let S be the set of all subsets of {0, 1, 2,3}. We define two weight functions w and w* as follows: For any XES, w(X) = Ei, w*(X) = II i, iEX iex with w() = w*() = 0. (a) Derive the generating series of S with respect to w and with w*. (b) Let T be the set of all subsets of {0, 1, 2, 3, ... }. Determine whether or not the generating series of T with respect to w and with w* are formal power series. Explain why