Consider the context-free grammar (S, Pl, a, b, c), R, S) where R is this set of rules: S -a ScSS SaPa PbPc (a) Write down a derivation tree for the string ccaabab. (b) Argue that there cannot be a derivation tree for any string starting with b. c) (A ittle harder.) Argue that the length of any derivable string (of terminals only) must be of the form 3n + 1 (i.e., 1, 4, 7, 10 etc.)