Question: Show that the following languages are not regular using Pumping Lemma. L_1 = {ww: w cap I {a, b}*} L_2 = {a^n b^l a^p: p

Show that the following languages are not regular using Pumping Lemma. L_1 = {ww: w cap I {a, b}*} L_2 = {a^n b^l a^p: p = n + l} (with n greaterthanorequalto 0, l greaterthanorequalto 0) 5.2.13 (P145) Find a Context free grammar for the language, L_3 = {a^n w w^R b^n: w elementof {a, b}*, n greaterthanorequalto 1} Suppose that the bowl contains many cookies. Some cookies are colored red and some are colored brown. 45% of the cookies in the bowl contain nuts, and 55% contain chocolate chips. 20% of cookies containing nuts are colored brown. 30% of cookies colored brown. What is the probability that a brown cookie contains nuts? (P (nuts | brown) =?)

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