Have main create two objects: setA and setB. Input the values into setA (end with a 0 or negative) and input the values into setB (end with 0 or negative).Print the ordered pairs using printOrderedPairs. Print if setA is a subset of setB. Then print if setA is a proper subset of setB.

C code is explained below

Explanation:

Sets.h:

#ifndef SETS_H

#define SETS_H

class Sets

{

    private:

         static const int s = 4;

         int na[s];

    public:

         //for constructor

         Sets();

         //function declaration for add the element

         void addElement(int);

         //function declaration for get the element

         int getElement(int);

         //function declaration for get size

         int getSize();

         //function declaration for check sub set

         bool isSubset(const Sets &);

         //function declaration for check the proper subset

         bool isProper(const Sets &);

         //function declaration for display the set

         void printSet();

         //function declaration for display the ordered set

         void Sets::printOrderedPairs( const Sets &);

};

#endif

Main.cpp:

#include "Sets.h"

#include <iostream>

using namespace std;

//constructor

Sets::Sets(){

   for (int i = 0; i < s; i++){

       na[i] = -1;

   }

}

//function definition for get size

int Sets::getSize(){

   return s;

}

//function definition for add the elements

void Sets::addElement(int l){

   for (int i = 0; i < s; i++){

       if (na[i] == -1){

           na[i] = l;

           break;

       }

   }

}

//function definition for get element

int Sets::getElement(int j){

   if (j < s){

       return (-1);

   }

   else{

       int t;

       t = na[j];

       return t;

   }

}

//function definition for check the subset

bool Sets::isSubset( const Sets &b ) {

  for (int i = 0, j = 0; i < b.s; i++ ) {

          while ( j < s && na[j] < b.na[i] ) ++j;

       if ( j == s || na[j] > b.na[i] )

           return false;

   }

   return true;

}

//function definition for check the proper subset

bool Sets::isProper( const Sets &b ) {

   int ne = 0;

   for (int i = 0, j = 0; i < b.s; i++ ) {

       while ( j < s && na[j] < b.na[i] ) ++j;

       if ( j == s || na[j] > b.na[i] )

           return false;

       ++ne;

   }

   return ne < s;

}

//function definition for display the ordered set

void Sets::printOrderedPairs( const Sets &b){

   cout << "A X B = {";

   for (int i = 0; i < s; i++){

       for (int j = 0; j < b.s; j++){

           cout << '(' << na[i] << ", " << b.na[j] << "), ";

     }

   }

   cout << "\b\b} ";

}

//function definition for display the set

void Sets::printSet(){

   cout << "{";

   for (int i = 0; i < s; i++){

       cout << na[i] << ",";

   }

   cout << "}";

}

//main function

int main()

{

   //object for Set A

   Sets a;

   //object for Set B

   Sets b;

   //add the element for Set A

   a.addElement(1);

   a.addElement(2);

   a.addElement(3);

   a.addElement(4);

    //add the element for Set B

   b.addElement(3);

   b.addElement(4);

   b.addElement(5);

   b.addElement(6);

   //display the set A

   cout << "Set A: ";

   a.printSet();

   cout << endl;

   //display the set B

   cout << "Set B: ";

   b.printSet();

   cout << "\n" << endl;

   //display the A X B

    a.printOrderedPairs(b);

   cout << "\n" << endl;

    //chrck the subset

   if (a.isSubset(b) == true){

       cout << "Set B is subset of set A" << endl;

   }

   else{

       cout << "Set B is not a subset of set A" << endl;

   }

    //check the proper subset

   if (a.isProper(b) == true){

       cout << "Set B is proper subset of set A" << endl;

   }

   else{

        cout << "Set B is not a proper subset of set A" << endl;

   }

   system("PAUSE");

   return 0;

}

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