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Give a regular expression for L_6 = {w epsilon {0,6}*: n_a(w) is odd and n_b(w) is even}. Find regular grammars for the following languages over sigma = {a, b}. L_4a = {w: |na(w) + n_b(w)| is odd}. L_4b = L(aa + ab + ba + bb)*. L_4c = {w - |n_a{w) - n_b(w)| is odd}. For each of the following languages, prove or disprove that it is regular. L_a = {uav:uv epsilon L}, where L is any regular language over {a, b}. L_b = {w:w epsilon {a, b}* and w = w^R}. Lc= {b^ka^nb^n:n,k ge 0}. L_d = {a^n: n is a prime number}