6) Closure Properties: a) Prove, using DFAs, that the class of regular languages is closed under the intersection operation. Note: This should be a formal proof. b) Given the DFA Mithat recognizes Li and M2 that recognizes L2, both on the next page; i. Write a 5-tuple defining the DFA M which recognizes the intersection of L1 and L2 by running Mi and M2. Thoroughly define each element of the tuple. ii. Draw the state diagram for M. The label for each state should be a pair of states. Give the computation in M for the string 100101. (See the definition of computation from notes or the text.) Is 100101 accepted by M? Is 100101 an element of Lun L2? Explain. iv. 1 c) Regular Languages are closed under set difference where set difference of two languages Li and L2 is defined to be the elements in L, that are not in L2 i. Write set difference symbolically using the other known closure properties. Explain how that proves that set difference is closed. ii. Write a 5-tuple defining the DFA M' which recognizes the set difference of L1 and L2. iii. Draw the state diagram for M'. The label for each state should be a pair of states. DO Mi: M2