Let = {a, b, } and let F = {w x | w, x {a, b} and w and x have the same number of as or the same number of bs} So, for example, aaa aa F because both w = aaa andx = aa have zero bs.

(a) Prove that F is not regular.

(b) Is F context-free? Prove your answer.

2. Let = {a, b,-) and let F = {w-z | w, z {a, b)' and to and r have the same number of a's or the same number of b's} So, for example, aaa-aa e F because both w aaa andr = aa have zero bs. (a) Prove that F is not regular. (b) Is F context-free? Prove your