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2. [20pt] Use the pumping lemma to prove that the following languages are not regular. In all cases, = {0.1): L,-(w | no(w) 2n1(w) where

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2. [20pt] Use the pumping lemma to prove that the following languages are not regular. In all cases, = {0.1): L,-(w | no(w) 2n1(w) where n() is the number of occurrences of r in (d) L,-(Hjgk l i, j, k > 0 and i + j = k} (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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