# include <iostream.h>

class Set {

public :
Set(){ N = 0; } // Default constructor
void add( Set& S, int x);
void Remove( Set& S, int x);
void print( );

private:
int N;
int e[20];

} ;

Third: This is the function "Remove" written after main() function

#include <iostream>
using namespace std;

class set
{
private:
int elements [20];
int N;

public:
set ();
void add (int); // add elements into the set
void remove ( int); // remove elements from the set
void printSet (); // print the elements of the set
bool isEmptySet (); // check if set is empty or not; if empty return true
set Union (set &); // perform a union between two sets
set intersection (set &); // perform an intersection between two sets
bool testIfSubset (set & ); // check if first set is subset in the second set


};

set::set ()
{
N = 0; // size of the set
for (int i =0; i<=19; i++)
elements[i] = 0;
}

void set::add(int e)
{
// check if the element fits in the set; i.e. if the set is full or not

if (N == 20) // means that the set is full
cout <<"The set is full"<<endl;

else // the set is not full
{
bool found = false; // element not found in set
for (int i = 0; i < N; i++)
{
if (e == elements[i]){
found = true; break;}
}
if (found)
cout <<"element found in the set";
else
{
elements[N] = e;
N++; // update the size of the set
cout <<"Element added"<<endl;
}

}
}

void set::remove(int e)
{
if (!isEmptySet ()) // set is not empty
{
// search for the position of the element

int position = -1;
for (int i = 0; i < N; i++)
{
if (elements[i] == e)
{
position = i;
break;
}
}
if (position != -1) // element found in the set at index position
{
elements[position]=elements[N-1];
N--; // update the size of the set
cout <<"element removed"<<endl;
}
else
cout <<e<<" is not an element in the set"<<endl;
}
else
cout <<"The set is empty; there is no elements found till yet"<<endl;
}

void set::printSet()
{
if (isEmptySet ())
cout <<"Set is empty"<<endl;
else
{
cout <<"Elements are:"<<endl;
for (int i = 0; i < N; i++)
cout <<elements [i]<<" ";
}
cout <<endl;
}

bool set::isEmptySet()
{
return N == 0;
}

set set::Union(set & s1)
{
set resultSet;

if (N == 0 && s1.N != 0) // if first set is empty and the second is not
for (int i = 0; i < s1.N ; i++)
resultSet.add(s1.elements[i]);
else if (N != 0 && s1.N == 0) // if second set is empty and the first is not
for (int i = 0; i < N; i++)
resultSet.add(elements[i]);
else if (N != 0 && s1.N != 0) // if two sets are not empty
{
// add elements of first set into result set

for (int i = 0; i < N; i++)
resultSet.add(elements[i]);

// check if there exists elements found in the second set that can be added to the result set

for (int i = 0; i < s1.N; i++)
{

resultSet.add(s1.elements[i]);
}
}
else // if two sets are empty
cout <<"Union between to (phi) sets is (phi)" <<endl;

return resultSet;
}

set set::intersection(set & s1)
{
set resultSet;

if (N != 0 && s1.N != 0) // if first set is empty and the second is not


// check if there exists elements found in the second set that can be added to the result set

for (int i = 0; i < N; i++)
{
bool found = false; // indicates that element is not found in the second set
for (int j = 0; j < s1.N; j++)
{
if (elements[i] == s1.elements[j])
{
found = true; // element in first set is found in the second set
break;
}
}
if (found)
resultSet.add(elements[i]);
}
}
else // if two sets are empty
cout <<"Intersection between the sets is impossible" <<endl;

return resultSet;
}

bool set::testIfSubset (set & s1)
{
Set rs = (*this).intersection(s1);
if (rs == *this)
return true;
else
return false;


}

void main ()
{
// --- testing the class --- //

int n;
set s1;

// add to set
cout <<"Enter a number to add to set (-5 to end): ";
cin >> n;
while (n != -5)
{
s1.add(n);
cout <<endl;
s1.printSet();
cout <<"Enter a number to add to set (-5 to end): ";
cin >> n;
}

// remove from set;
system("cls");
s1.printSet();
cout <<"Enter a number to remove from set (-5 to end): ";
cin >> n;
while (n != -5)
{
s1.remove(n);
cout <<endl;
s1.printSet();
cout <<"Enter a number to remove from set (-5 to end): ";
cin >> n;
}

system("cls");

// testing union, intersection and subset
cout <<"Elements of set 1 are"<<endl;
s1.printSet();

set s2;
for (int i = 1; i <= 10; i++)
s2.add(i * 2 - 3);
cout <<"Elements of set 2 are"<<endl;
s2.printSet();

set r1, r2;
r1 = s1.Union(s2);
r1.printSet();

r2 = s1.intersection(s2);
r2.printSet();

if (s1.testIfSubset(s2))
cout <<"s1 is subset of s2"<<endl;
else
cout <<"s1 is not subset of s2"<<endl;
}