(30 point) For each i=1,2 and 3, compose a regular expression Ri, such that L(Ri) = Ci, where

(a) C1 = {w|w has an odd number of 00s, or, contains exactly three 10s}.

(b) C2 = {w|the length of w is at most 5}.

(c) C3 = {w|all strings except the strings }11 and 111.

Give reason(s) to support your answer to each case. The reason(s) given for each case should be concise. Do not use more than three complete sentences for each case.

Thanks!