3. [10pt] Show that the class of regular languages is closed under complement. Hint: Prove that given a DFA M that accepts a language L(M) CE", swapping the accept and nonaccepting states in M yields a new DFA M' recognizing the complement of L(M), i.e., L(M') = L(M) = 5* L(M). 4. [5pt] Given two sets A and B, we define the binary set difference operation as follows A - B = {w We A and wB} = AB, Prove that the class of regular languages is closed under the set difference operation. 3. [10pt] Show that the class of regular languages is closed under complement. Hint: Prove that given a DFA M that accepts a language L(M) CE", swapping the accept and nonaccepting states in M yields a new DFA M' recognizing the complement of L(M), i.e., L(M') = L(M) = 5* L(M). 4. [5pt] Given two sets A and B, we define the binary set difference operation as follows A - B = {w We A and wB} = AB, Prove that the class of regular languages is closed under the set difference operation