I. Consider the following context free grammar G-(IS, A, a, b, ta, b). R, S), where R- S-a ASS A-ba (a) Answer each of the following questions True or False: (i) From the fact that G is context free, it follows that there is no regular expression for L/G) (ii) L(G) contains no strings of length 3. (iii) For any string we L(G), there exists u, v, x, y, z such that w uvxyz, vy2 1, and uv y'zE L(G) for all n 20 (iv) If there exist languages L1 and L2 such that LAG)-LI u L2, then L1 and L2 must both be context free. (v) The language (L(G) is context free. (b) Give a leftmost derivation according to G of aaaabaa. (c) Give the parse tree corresponding to the derivation in (b) Consider the following PDA: 91 (a) Show that the PDA accepts the word aaadbabacc