Consider the context-free grammar ({S, P}, {a,b,c}, R, S) where R is this set of rules: S S S P a CSSb a Pa bPc (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 little 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.).