Let = {0, 1, #}, and let B = {w#w | w {0, 1} }.

(a) Complete the following statement: if a, b, c, and d are positive integers, then (0^a)(1^b)#(0^c)(1^d) B iff

(b) Use the Pumping Lemma for context-free languages to prove that B is not context-free. Hint: break into two cases, based on whether the pumping substring vxy includes the # symbol or not.

(c) [10 extra points] Let F = {w#q | w, q {0, 1}^ and w 6= q}. Prove or disprove that F is context-free.