Problem A. Following is an incomplete non-regularity proof that uses the minimum state lemma. Give an appropriate answer for each blank in the given incomplete proof. For each blank, write a string precisely using the alphabet {a,b,c and possibly integer variables and constants, for example a99bc3yk, except for blank (2), where a conditional expression involving the variables used in blank (1) is expected. Type your answer for each blank on an answer sheet. The language L1= {c' a" b1 i, n > 0 } is not regular as proved below. Consider the infinite set D={ (1) (2) }. For an arbitrary pair of strings (3) and (4) from D such that x y, the string (5) is a distinguisher because the string _(6) E Ll, but the string (7) L1. Hence, the strings in D are pairwise distinguishable with respect to L1. Thus, by the minimum state lemma, L1 is not regular Problem A. Following is an incomplete non-regularity proof that uses the minimum state lemma. Give an appropriate answer for each blank in the given incomplete proof. For each blank, write a string precisely using the alphabet {a,b,c and possibly integer variables and constants, for example a99bc3yk, except for blank (2), where a conditional expression involving the variables used in blank (1) is expected. Type your answer for each blank on an answer sheet. The language L1= {c' a" b1 i, n > 0 } is not regular as proved below. Consider the infinite set D={ (1) (2) }. For an arbitrary pair of strings (3) and (4) from D such that x y, the string (5) is a distinguisher because the string _(6) E Ll, but the string (7) L1. Hence, the strings in D are pairwise distinguishable with respect to L1. Thus, by the minimum state lemma, L1 is not regular