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 H(M). 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 your answer. (Hint: The halting problem is similar to the universal language).