Problem 2. [50 points] For each of the following languages, determine whether it is regular and prove that your answer is correct: {wwT: We {0, 1}*}; {0a150 : a+b=c}; The language of strings over {0,1} that contain an equal number of occurrences of 01 and 10 or, more formally, {ao --- An-1 {0,1}* : |{i {0,..., n 2} : QiQit1 = 01} = l{i {O..., n 2}: ;dit1 = 10}]}; The language of strings over {0, 1, 2} that contain an equal number of occurrences of 01 and 10 or, more formally, {ao --- An-1 {0, 1, 2}* : |{i {O,.., n 2} : a;dit1 = 01} ={i {0,...,n 2} : ;dj +1 = 10}|}; and Lo ...On-1 {0M1":m=n}. Problem 2. [50 points] For each of the following languages, determine whether it is regular and prove that your answer is correct: {wwT: We {0, 1}*}; {0a150 : a+b=c}; The language of strings over {0,1} that contain an equal number of occurrences of 01 and 10 or, more formally, {ao --- An-1 {0,1}* : |{i {0,..., n 2} : QiQit1 = 01} = l{i {O..., n 2}: ;dit1 = 10}]}; The language of strings over {0, 1, 2} that contain an equal number of occurrences of 01 and 10 or, more formally, {ao --- An-1 {0, 1, 2}* : |{i {O,.., n 2} : a;dit1 = 01} ={i {0,...,n 2} : ;dj +1 = 10}|}; and Lo ...On-1 {0M1":m=n}