2. (a) Give an example of two uncountable sets A and B with a nonempty intersection, such that A-B is 1. finite ii. countably infinite iii. uncountably infinite 13. 4] is uncountable. 3, 4] is uncountable. (You can use the fact that the set of rational numbers (Q) is countable and (b) Use the Cantor diagonalization argument to prove that the number of real numbers in the interval (c) Use a proof by contradiction to show that the set of irrational numbers that lie in the interval the set of reals (R) is uncountable). Show all work. 2. (a) Give an example of two uncountable sets A and B with a nonempty intersection, such that A-B is 1. finite ii. countably infinite iii. uncountably infinite 13. 4] is uncountable. 3, 4] is uncountable. (You can use the fact that the set of rational numbers (Q) is countable and (b) Use the Cantor diagonalization argument to prove that the number of real numbers in the interval (c) Use a proof by contradiction to show that the set of irrational numbers that lie in the interval the set of reals (R) is uncountable). Show all work