Problem 2. (Write a Regular Expressions) (3 marks) Show that the following languages are regular by giving a regular expression that describes each one: L1= {all strings over 2 = {0,1} containing at least two o's). Solution: 1) r=1'01*0(0+1) 2)DFA: 0 90 91 a) L2= {all strings over x = {0,1} containing at most four 1's). b) L4 = {all strings over = {0,1} that contain the substring 10 and the substring 01). c) L5 = {all strings over 9 = 0, 1) that does not contain the substring 101). d) 1.8 = {all strings over = {a,b,c) with length greater than two). e) 19 = (all strings over 9 = a,b,c) in which the number of b's is divisible by 4). 1) L10=fall strings over ) = (a,b,c) in which the total number of a's and e's is 2). mar