2. Let FIN-(M | L(M) is finite), and recall HP-(M#w 1 M halts on w} (a) Prove HP Sm FIN, where HP is the complement of the halting problem. That is, show there exists a computable function f such that M#w e HP iff f(M#w) e FIN. [5 (b) Prove HP Sm FIN. That is, show there exists a computable function f such that (c) Is FIN decidable? Is it recognizable? Justify your answer. [5]