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1. ( 30 points) Write a computer program that finds the first 20 numbers of the Fibonacci sequence and puts into a list. 2. (50 points) Write a computer program that defines the class "Set" (assume that the elements are integers). The class should contain methods to perform the operations listed below. Write a test program that tests your "Set" class. a) Different constructors to initialize the set (one is to set the elements from a one-dimension array) b) union: find the union of the set with a given set. OUTPUT: a Set object. c) intersection: find the intersection of the set with a given set. OUTPUT: a Set object. d) difference: find the difference of the set and the given set (Set - given Set). OUTPUT: a Set object. e) Cartesian product: find the Cartesian product (Set X given set). OUTPUT: prints out the product. f) Check whether the set is a subset of another set. OUTPUT: True or False. 8) Find the powerset of the set. OUTPUT: prints out the powerset. h) isEmpty method that returns true if the set is empty (no elements). i) isElement method that takes an element and check if it is an element of the set. j) isEqual method that check if the set is equal to a given set. k) getCardinality method that returns the cardinality of the set. I) addElement method that adds element to the set. Make sure that you don't add an existing element. You will use isElement check before you try to add it. m) removeElement method to remove an element from the set. n) Clear method to remove all elements of the set. o) toArray that converts the object of the Set class to a one-dimensional array. p) print method to print the elements of the set. In your test program, declare two sets objects and use the constructor to initialize them by sending a onedimension array contains the elements of the set. 3. ( 10 points) Prove that 3n<>