Give to-the-point answers, and do not write more than the space provided, otherwise great penalties apply 1). Let L be a recursively enumerable language and L is not empty. Is there a subset of L that is recursive? Prove or disprove it. (10 pts) 2). Let H(M) be the set of inputs w such that M halts given input w. The halting problem is the set of pairs (M, w) such that w is in HM). Prove that the halting problem (the set of pairs) is recursively enumerable, but not recursive. Is it possible to write a C compiler that will tell whether a C program will always terminate on any input? Justify you answer. (Hint: The halting problem is similar to the universal language.) (20 pts)