For the following questions, the alphabet is{a, b, c}.

= 2. Consider the regular language L {w | w does not contain the substring aba}. (a) (5 points) Why is 4 a valid choice of pumping length p for L? (b) (10 points) Let w abbbb. Give x, y, and z such that all of the following hold, and explain why condition (iv) holds for your choice of x, y and z. = i. W = xyz ii. xyl 0 iv. for all i EN, xy'z E L. (c) (10 points) Let w = aabb. Give x, y, and z such that the above conditions all hold, and explain why condition (iv) holds