2. (a) Prove that * is countably infinite for any nonempty, finite alphabet E. (b) Deduce from (a) that the set of all possible Microsoft PowerPoint presentations is countable. (c) Deduce from (b) that the set of Turing Machines over a given alphabet & is countable. Hint: https://youtu.be/uNjxe8ShM-8 (d) Prove that the set of all decidable languages over a given alphabet & is countable. (e) Conclude that there are more undecidable languages than decidable languages over a given alphabet . 2. (a) Prove that * is countably infinite for any nonempty, finite alphabet E. (b) Deduce from (a) that the set of all possible Microsoft PowerPoint presentations is countable. (c) Deduce from (b) that the set of Turing Machines over a given alphabet & is countable. Hint: https://youtu.be/uNjxe8ShM-8 (d) Prove that the set of all decidable languages over a given alphabet & is countable. (e) Conclude that there are more undecidable languages than decidable languages over a given alphabet