Question: 1. (Non-regular languages) Prove that the following languages are not regular. You may use the pumping lemma and the closure of the class of regular

1. (Non-regular languages) 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, complement, and reverse.

(c) L3 = {1ky | y {0, 1}* and |y| = k }.

(d) L4 = {aibjck | i,j,k 0 and if i = 1 then j = k }.

(e) L4 satisfies conditions of the pumping lemma. Explain why this does not contradict the fact that L4 is not regular.

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