java

Write each of the following pure functions (a function is pure if it does not update any of the arguments or global variables). The actual return type Set should be the same as the actual type of the parameter Set. subset(s1, s2) is true iff s1 is a subset of s2. public static boolean subset (Set si, Set s2) union(s1, s2) returns the union of si and s2. public static Set union(Set si, Set s2) intersection (s1, s2) returns the intersection of si and s2. public static Set intersection (Set si, Set s2) difference (s1, s2) returns the difference of s1 and s2 (i.e., s1 s2) public static Set difference (Set si, Set s2) cartesianProduct(s1,s2) returns the Cartesian product of s1 and s2. public static ArrayList> cartesianProduct(Set si, Set s2) where Pair is defined as follows: class Pair public u first; public V second; public Pair(U first, V second) { this.first = first; this second = second; } The following implementation of the function removeDuplicates (list) does not scale well due to its quadratic time complexity. 1 public static ArrayList removeDuplicates (ArrayList list) { ArrayList newList - new ArrayList(); for(int i = 0; i