set's Introduction

Set

You may use any function or library discussed in class or in the chapters we covered from your textbook. Do not use any other libraries or functions.

Design a C++ class that stores a mathematical set of integers called MySet (do not use a different name). The class should be stored in "myset.h" and include the following functions:

A default constructor that initializes a set to the empty set.
Overload the "^" operator to implement the set membership. Returns true if an element is in the set.
Overload the "+" operator to add an element to the set. Return the original set with the new element added.
Overload the "-" operator to remove an element from the set. Return the original set with the new element removed.
Overload the "+" operator to implement the union of two sets. Returns a new set that contains all the elements of both sets.
Overload the "*" operator to implement the intersection of two sets. Returns a new set that contains all the elements that are in both sets.
Overload the "-" operator to implement the set difference. Returns a new set that contains all the elements that are in the first set but not in the second.
Overload the "<=" operator to implement the subset. Returns true if all the elements of the first set are in the second.
Overload the ">=" operator to implement the superset. Returns true if all the elements of the second set are in the first.
Overload the "==" operator to implement the set equality. Returns true if both sets contain the same elements (in any order).
A function called toString that returns a set string in the format "{1, 2, 3, 4}"). The set elements must be sorted.
A function to return the number of elements in the set (size).
A function to clear the set by removing all the elements (clear).