Write a class ++ IntSet for modeling sets of integers in the range 0 through 99. A set should be represented internally as an array of type bool: The i^th array element will be true whenever integer i is in the set and will be false whenever integer i is not in the set. Include a no-argument constructor that initializes a set to the so-called empty set, i.e., a set whose array representation contains all false values. The class should include the following overloaded operators:

+ to perform the union of two set (the union of sets A and B is the set that contains all

elements of set A or set B, or both).

* to perform the intersection of two sets (the intersection of sets A and B is the set that

contains all elements in both set A and set B.)

- to form the difference of two sets (the difference of sets A and B is the set containing those elements that are in A but not in B)

+= to add an integer into a set.

-= to delete an integer from a set.

== to determine if two sets are equal.

! to form the complement of a set (the complement of set A, denoted , is the set containing all the elements in the universal set that are not in A - the universal set for this problem is the set containing all integers between 0 and 99)

<= to determine if one set is a subset of another set (set A is a subset of set B means that for any element x in A, x is also an element of set B).

<< to display a set in roster notation (for example, {2, 3, 5, 9})

Requirement: The overloaded += and -= operators should check for valid integer input (in the range 0-99), or if an add-item is already in the set, or if a delete-item is not in the set. An error message for invalid input should be generated.

Then, write a C++ program that uses the new IntSet class. The program should allow the user to repeatedly select from these options:

add numbers to a set

remove numbers from a set

form the union of two sets

form the intersection of two sets

form the difference of two sets

determine if two sets are equal

form the complement of an set

determine if one set is a subset of another set

display a set

The program should allow for up to ten sets to be created during a given program run. Use any stand-alone functions you feel necessary.

Here is output from a sample run of the program (user input in bold):

Select an option:

- add numbers to a set

- remove numbers from a set

- form the union of two sets

- form the intersection of two sets

- form the difference of two sets

- determine if two sets are equal

- form the complement of an set

- determine if one set is a subset of another set

- display a set

Exit

1

Add numbers to which sets (A, B,C, D, E, F, G, H, I, J)? :A

Enter number to add: 1

Add another (y or n): y

Enter number to add: 3

Add another (y or n): y

Enter number to add: 8

Add another (y or n): n

Select an option:

- add numbers to a set

- remove numbers from a set

- form the union of two sets

- form the intersection of two sets

- form the difference of two sets

- determine if two sets are equal

- form the complement of an set

- determine if one set is a subset of another set

- display a set

Exit

9

Display set (A, B, C, D, E, F, G, H, I, J)? :A

{1, 3, 8}

Select an option:

- add numbers to a set

- remove numbers from a set

- form the union of two sets

- form the intersection of two sets

- form the difference of two sets

- determine if two sets are equal

- form the complement of an set

- determine if one set is a subset of another set

- display a set

Exit

1

Add numbers to which sets (A, B,C, D, E, F, G, H, I, J)? :B

Enter number to add: 2

Add another (y or n): y

Enter number to add: 3

Add another (y or n): y

Enter number to add: 7

Add another (y or n): n

Select an option:

- add numbers to a set

- remove numbers from a set

- form the union of two sets

- form the intersection of two sets

- form the difference of two sets

- determine if two sets are equal

- form the complement of an set

- determine if one set is a subset of another set

- display a set

Exit

2

Remove numbers from which set (A, B, C, D, E, F, G, H, I, J)? :A

Enter number to remove: 1

Remove another (y or n): n

Select an option:

- add numbers to a set

- remove numbers from a set

- form the union of two sets

- form the intersection of two sets

- form the difference of two sets

- determine if two sets are equal

- form the complement of an set

- determine if one set is a subset of another set

- display a set

Exit

3

Sets union specify sets to use:

First set: (A, B, C, D, E, F, G, H, I, J)? :A

Second set: (A, B, C, D, E, F, G, H, I, J)? :B

Result set: (A, B, C, D, E, F, G, H, I, J)? :C

Select an option:

- add numbers to a set

- remove numbers from a set

- form the union of two sets

- form the intersection of two sets

- form the difference of two sets

- determine if two sets are equal

- form the complement of an set

- determine if one set is a subset of another set

- display a set

Exit

4

Set intersection specify sets to use:

First set: (A, B, C, D, E, F, G, H, I, J)? :A

Second set: (A, B, C, D, E, F, G, H, I, J)? :B

Result set: (A, B, C, D, E, F, G, H, I, J)? :D

Select an option:

- add numbers to a set

- remove numbers from a set

- form the union of two sets

- form the intersection of two sets

- form the difference of two sets

- determine if two sets are equal

- form the complement of an set

- determine if one set is a subset of another set

- display a set

Exit

5

Set difference specify sets to use:

First set: (A, B, C, D, E, F, G, H, I, J)? :A

Second set: (A, B, C, D, E, F, G, H, I, J)? :B

Result set: (A, B, C, D, E, F, G, H, I, J)? :E

Select an option:

- add numbers to a set

- remove numbers from a set

- form the union of two sets

- form the intersection of two sets

- form the difference of two sets

- determine if two sets are equal

- form the complement of an set

- determine if one set is a subset of another set

- display a set

Exit

6

Set equality specify sets to compare:

First set: (A, B, C, D, E, F, G, H, I, J)? :A

Second set: (A, B, C, D, E, F, G, H, I, J)? :B

These sets are not equal

Select an option:

- add numbers to a set

- remove numbers from a set

- form the union of two sets

- form the intersection of two sets

- form the difference of two sets

- determine if two sets are equal

- form the complement of an set

- determine if one set is a subset of another set

- display a set

Exit

7

Set complement specify sets to use:

Complement set: (A, B, C, D, E, F, G, H, I, J)? :A

Result set: (A, B, C, D, E, F, G, H, I, J)? :F

Select an option:

- add numbers to a set

- remove numbers from a set

- form the union of two sets

- form the intersection of two sets

- form the difference of two sets

- determine if two sets are equal

- form the complement of an set

- determine if one set is a subset of another set

- display a set

Exit

8

Subsets specify sets to compare:

First set: (A, B, C, D, E, F, G, H, I, J)? :A

Second set: (A, B, C, D, E, F, G, H, I, J)? :B

The first set is not a subset of the second

Select an option:

- add numbers to a set

- remove numbers from a set

- form the union of two sets

- form the intersection of two sets

- form the difference of two sets

- determine if two sets are equal

- form the complement of an set

- determine if one set is a subset of another set

- display a set

Exit

9

Display set (A, B, C, D, E, F, G, H, I, J)? :B

{2, 3, 7}

Select an option:

- add numbers to a set

- remove numbers from a set

- form the union of two sets

- form the intersection of two sets

- form the difference of two sets

- determine if two sets are equal

- form the complement of an set

- determine if one set is a subset of another set

- display a set

Exit

10