3. Find minimal dfa's for the following languages. In each case, prove that the result is minimal. (a) L = {alm : n 2 1, m 2 2}. (b) L = {a"b: n 2 1}v{ba : n 2 1}. (c) L = {a" : n 2 0, n = 2}. (d) L = {a": n + 3 and n = 4). (e) L = {a": n mod 3 = 1}~{a": n mod 5 = 1}