Question 7:

a) Let L₃ = {1ⁿ0^k1⁴ⁿ | n 0, k > 0}. Prove thatd there is no DFA M₃ for L₃ such that L(M₃) = L₃

b) Let L₄ = {a, b} \ {waw_R | w is any string over {a, b}} be a language over = {a, b}. Prove that there is no DFA M₄ such that L(M₄ ) = L₄. Your proof should be short and not use the Pumping Lemma.