Which of the following problems about Turing machines are solvable, and which are undecidable? Explain your answers carefully. (a) To determine, given a Turing machine M, a state q, and a string w, whether M ever reaches state q when started with input w from its initial state. (b) To determine, given a Turing machine M and a symbol a, whether M ever writes the symbol a when started with the empty tape. Which of the following problems about Turing machines are solvable, and which are undecidable? Explain your answers carefully. (a) To determine, given a Turing machine M, a state q, and a string w, whether M ever reaches state q when started with input w from its initial state. (b) To determine, given a Turing machine M and a symbol a, whether M ever writes the symbol a when started with the empty tape