(12 pts.) The order of a regular nonempty language L is defined to be the smallest integer k for which L+ if there is such a k, and oo otherwise. (a) Show that the order of L is finite if and only if there is an integer k so that LL* and in this case the order of L is the smallest k such that LkL (b) Find the order of the regular language (A) U [aa aaa, and justify it