Let FIN = {M | L(M) is finite), and recall HP = {M#w | M halts on w} FIN, where HP is the complement of the halting problem. That is, show there exists a computable function f such that M#ue HP iff f(M#u) 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 Let FIN = {M | L(M) is finite), and recall HP = {M#w | M halts on w} FIN, where HP is the complement of the halting problem. That is, show there exists a computable function f such that M#ue HP iff f(M#u) 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