*! Exercise 4.2.2: If L is a language, and a is a symbol, then L/a, the quotient of L and a, is the set of strings w such that wa is in L. For example, if L = {a, aab, baa), then L/a = {e,ba). Prove that if L is regular, so is L/a. Hint: Start with a DFA for L and consider the set of accepting states ! Exercise 4.2.3: If L is a language, and a is a symbol, then a\L is the set of strings w such that aw is in L. For example, if L = {a, aab, baa), then a\L = {e, ab). Prove that if L is regular, so is a\L. Hint: Remember that the regular languages are closed under reversal and under the quotient operation ot Exercise 4.2.2. ! Exercise 4.2.4: Which of the following identities are true? a) (L/a)a = L (the left side represents the concatenation of the languages L/a and (a). b) a(a\L) = L (again, concatenation with {a), this time on the left, is intended) c) (La)/a L d) al(al)= L