2.8. Let M = (Q, E, 90, A, 8) be an FA. Below are other conceivable methods of defining the extended transition function 8* (see Definition 2.12). In each case, determine whether it is in fact a valid definition of a function on the set Q x 2*, and why. If it is, show using mathematical induction that it defines the same function that Definition 2.12 does. a. For every q Q, 8*(q, A) = q; for every y *, o E E, and q E Q, 8*(q, yo) = 8*(8*(q, y), o)