Use the pumping lemma to show that each of these languages is nonregular:
(i) {aⁿbⁿ⁺¹} = {abb aabbb aaabbbb . . .}
(ii) {aⁿbⁿaⁿ} = {aba aabbaa aaabbbaaa aaaabbbbaaaa . . .}
(iii) {aⁿb²ⁿ} = {abb aabbbb aaabbbbbb . . .}
(iv) {aⁿbaⁿ} = {aba aabaa aaabaaa . . .}
(v) {aⁿbⁿa^m where n = 0, 1 , 2, . . . and m = 0, 1 , 2, . . . } = {Λ a aa ab aaaaba . . . }