Question: 2. [20pt] Prove that the following languages are not regular. You may use the pumping lemma and the closure of the class of regular languages

 2. [20pt] Prove that the following languages are not regular. You

2. [20pt] Prove that the following languages are not regular. You may use the pumping lemma and the closure of the class of regular languages under union, intersection, and complement. In all cases. = {0,1}: (a) L1 = {www | W 3*} (b) L2 = {w the number of occurrences of 00 is the same as the number of occurrences of 11 in w} (c) L3 = {w now) 0} (Hint: If you need some practice with pumping lemma-related problems, JFLAP has some examples for the pumping lemma. From the JFLAP menu, choose Regular Pumping Lemma to see some examples of regular and non-regular languages.) 2. [20pt] Prove that the following languages are not regular. You may use the pumping lemma and the closure of the class of regular languages under union, intersection, and complement. In all cases. = {0,1}: (a) L1 = {www | W 3*} (b) L2 = {w the number of occurrences of 00 is the same as the number of occurrences of 11 in w} (c) L3 = {w now) 0} (Hint: If you need some practice with pumping lemma-related problems, JFLAP has some examples for the pumping lemma. From the JFLAP menu, choose Regular Pumping Lemma to see some examples of regular and non-regular languages.)

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