2. Let M be the pushdown automata (PDA) defined as: M = ({90, 91, 92}, {a, b, c}, {A}, 6, 90, {92}) 8: 8(90, 0, 1) = {[90, A]}; 8(91, 1, 1) = {[92, A]}; 8190, b, A) = {[91,2]}; 8(92, C, 1) = {[92, X]}. 8(91, b, A) = {[q1, 2]}; Give the state diagram for the PDA Mi. Trace all computations of strings aabbc, abbc, ab in M. Give a set-theoretic definition of the language accepted by M. Write a grammar for the corresponding PDA. Write the shortest string that is IN and NOT IN the language L(M). a) b) c) d) e)