Need help with Combinatorics Problem!!!!

Let A and B be subsets of strings such that AB and A* are unambiguous expressions. We have learned these two rules when the weight of a string is its length: (131430;) = '13,; (x)3(x) and (Prat) = (1 (13A (JIc))_1 . For each of the following, we define a new weight function L0\" for a string. Determine whether or not these two rules can still be applied when we use w"' as the weight function. If so, then explain why we can do so, and determine the generating series of S below with respect to W". If not, give a general explanation of why we cannot apply one of the rules, and give an example where the rule fails. S = {1}*({000}{1,11})*- (a) The weight of a string is the length of the string plus 2. (b) The weight of a string is the number of 1's in the string. (c) The weight of a string is the number of 0's plus three times the number of 1's