Write a C++ program that does the following:

1. Prompts the user for, and accepts a list of elements on a single line (separated by spaces). The elements are strings (with no embedded spaces). This is set A.
2. Prompts the user for, and accepts a second list of elements on a single line (separated by spaces). The elements are strings (with no embedded spaces). This is set B. Sets A and B will contain no more than 25 elements each.
3. Display each of the following.
   1. The cardinality and roster of the intersection of A and B
   2. The cardinality and roster of the union of A and B
   3. The cardinality and roster of the relative complement of A and B (i.e. A - B)
   4. The cardinality and roster of the relative complement of B and A (i.e. B - A)
   5. The cardinality and roster of the cross product of A and B
   6. The cardinality of the power set of the cross product of A and B (just the cardinality, not the roster.)

Do not use any C++ libraries to implement the intersection ,union, difference etc. operations. You must write your own routines for these. You can use the C++ library for strings.

This is the sample output:

Input the items in set A, separated by spaces. When you are done hit return.

discrete math CS251 pcc ****

The following is a list of the items in set A. A contains 5 items.

A = { discrete math CS251 pcc **** }

Input the items in set B, separated by spaces. When you are done hit return.

CS251 pcc &&&& qwerty

The following is a list of the items in set B. B contains 4 items.

B = { CS251 pcc &&&& qwerty }

A intersect B contains the following

{CS251 pcc }

The cardinality of the intersection is 2

A U B contains the following

{discrete math CS251 pcc **** &&&& qwerty }

The cardinality of the union is 7

A - B = { discrete math ****}

The cardinality is 3

B - A = { &&&& qwerty}

The cardinality is 2

The cardinality of A X B is 20

A X B contains {(discrete, CS251 ) (discrete, pcc ) (discrete, &&&& ) (discrete, qwerty ) }

(math, CS251 ) (math, pcc ) (math, &&&& ) (math, qwerty ) }

(CS251, CS251 ) (CS251, pcc ) (CS251, &&&& ) (CS251, qwerty ) }

(pcc, CS251 ) (pcc, pcc ) (pcc, &&&& ) (pcc, qwerty ) }

(****, CS251 ) (****, pcc ) (****, &&&& ) (****, qwerty ) }

The cardinality of the power set of the cross product is 1048576