2. In this problem, we will look at countability and cardinality of sets (a) Show that there are as many positive even numbers, 2,4,6,... as the natural numbers, 1,2,3 (b) Show that the set (,11is cuntable. (c) Show that the set of all programs in MATLAB is countable. (d) Show that the set of all Turing Machines is countable. (e) Prove that the union of two countable sets is countable. (f) Use part (e) to show that the set of irrational numbers is uncountable ten