2. [10 points] Consider the following two languages over -{a,b), L2- {re * 1 1 #a (u) _ #b(u)| 2 for every prefix u ofz), where #c(w) denotes the number of occurrences of the symbol c in the string w. Investigate the regularity of each of the languages. Prove your answers. Notes: For proving regularity using finite automaton (deterministic or nondeterministic), the state-transition diagram and interpretation of the states of the machine are sufficient For proving non-regularity, you must employ pumping lemma for regular languages. 2. [10 points] Consider the following two languages over -{a,b), L2- {re * 1 1 #a (u) _ #b(u)| 2 for every prefix u ofz), where #c(w) denotes the number of occurrences of the symbol c in the string w. Investigate the regularity of each of the languages. Prove your answers. Notes: For proving regularity using finite automaton (deterministic or nondeterministic), the state-transition diagram and interpretation of the states of the machine are sufficient For proving non-regularity, you must employ pumping lemma for regular languages