5. (a) Use the Pumping Lemma for Context-Free Languages to prove that if B is any infinite context free language, then B contains strings whose lengths form an infinite arithmetic progression whose common difference is at most the pumping length p of B. (b) Show that in the sequence of powers of two, 1,2,22,23,, there is no arithmetic progression of length 3 or more. (c) Use parts (a) and (b) of this exercise to prove that the language B={a2n:n0} over ={a} is not context-free