Q1. Let us define a new operation over two languages L1 and L2 and call it as Modified-Intersection. We will denote this operation as MI (L1, L2). It is defined to be the set of strings that are in L1 or L2, but not in both. For example, if L1 = {aa, abb} and L2 = {bb, abb, cc}, then MI (L1, L2) = {aa, bb, cc}. (a) Suppose L1 = {w | w (a*b*)} , L2 = {w | w (b*a*)}, and L3 = {w MI(L1, L2) | length of w 3}. Enumerate strings in L3. (b) For L1 and L2 defined in part (a) above, write a regular expression for the language of MI (L1, L2). (c) For any two languages L1 and L2, give a formula for MI (L1, L2) in terms of other set operations. You can use any of the following set operations: U (union), (intersection), - (set difference). (d) TRUE/FALSE: "For any two languages L1 and L2, MI (L1, L2) will always be a CFL". If TRUE, prove it formally. If FALSE, give a counter example to prove it.