Problem 3: Complement and Intersection (a) Use the results of homework 2 problem 5(a) to prove that Regular Languages are closed under complement. (b) Note that for any sets S, and S2, the intersection of S, and S2 is equal to complement of (Si' U S2'), where Si'is the complement of Sy and S2' is the complement of S2. Use this fact, as well as the results of part (a) to prove that Regular Languages are closed under intersection Problem 5 (Complement) a) Let M be some DFA (Q, S, d, 40, F). We create a DFA M' by swapping the accept and reject states of M, so that M'=(Q, S, d, 40, Q-F). Prove that L(M) is the complement of L(M), where the complement of a language Lis S*- L