conjuntos con mapas hash,HashSet, y set

conjuntos donde se añade elementos de A y B y luego se haya el complemento, la union la interseccion etc utilizando hasthset. para esto primero creamos una clase llamada hast y ponemos el siguiente codigo:

import java.util.HashSet;
import java.util.LinkedList;
import java.util.Set;
import javax.swing.JOptionPane;

/**
 *
 * @author andres2288
 */
public class hast {
  
    
    public  static void  ingresa (){
          Set h=new HashSet();
    h.add("hola");
    h.add("como estas");
     h.add("hola");
     
     for(String x:h)
            System.out.println("x"+x);
    
    }
      public Set ACOMPLEMENTOUsetomaUcomouniverso(LinkedList A,LinkedList B){
         Set h=new HashSet();
          
          
       for(String x:B){
             int cont=0;
       for(String y:A){
       if(x.equals(y)){
         //  JOptionPane.showMessageDialog(null, x);
   cont+=1;
       }
      
       }
       if(cont==0){
        h.add(x); 
        cont=0;
       }
       }
     
        return h;   
      }
     public Set AsubconjuntoB(LinkedList A,LinkedList B){ 
      Set h=new HashSet();
             
       for(String x:B){
      
       for(String y:A){
       if(x.equals(y)){
         //  JOptionPane.showMessageDialog(null, x);
           h.add(x); 
       }
      
       }
       }
     
        return h;    
     }
     public Set AinterseccionB(LinkedList A,LinkedList B){
      Set h=new HashSet();
             
       for(String x:A){
      
       for(String y:B){
       if(x.equals(y)){
         //  JOptionPane.showMessageDialog(null, x);
           h.add(x); 
       }
      
       }
       }
     
        return h;
     }
          public Set AdiferenciasimetricaB(LinkedList A,LinkedList B){
           Set h=new HashSet();
          
          
       for(String x:A){
             int cont=0;
       for(String y:B){
       if(x.equals(y)){
         //  JOptionPane.showMessageDialog(null, x);
   cont+=1;
       }
      
       }
       if(cont==0){
        h.add(x); 
        cont=0;
       }
       }
       // ahora miramos el b
       
       for(String x:B){
             int cont=0;
       for(String y:A){
       if(x.equals(y)){
         //  JOptionPane.showMessageDialog(null, x);
   cont+=1;
       }
      
       }
       if(cont==0){
        h.add(x); 
        cont=0;
       }
       }
     
        return h;   
              
          }
       public Set AdiferenciaB(LinkedList A,LinkedList B){
     Set h=new HashSet();
          
          
       for(String x:A){
             int cont=0;
       for(String y:B){
       if(x.equals(y)){
         //  JOptionPane.showMessageDialog(null, x);
   cont+=1;
       }
      
       }
       if(cont==0){
        h.add(x); 
        cont=0;
       }
       }
     
        return h;
       }
    public Set AUnionB(LinkedList A,LinkedList B){
    Set h=new HashSet();
        for (int i = 0; i < A.size(); i++) {
           h.add(A.get(i));
            
        }
  
    for (int i = 0; i < B.size(); i++) {
           h.add(B.get(i));
            
        }
    return h;
    }
    
     public static void main(String[] args) {
       ingresa ();  
     }
}

luego creamos un jframe veanse del siguiente codigo e imagen para guiarse, para saber ustedes que deben agregar que botones ,textos y areas en el jframe deben agregar

import java.util.HashSet;
import java.util.LinkedList;
import java.util.Set;

/**
 *
 * @author andres2288
 */
public class visual extends javax.swing.JFrame {
hast t =null;
    LinkedList listaA= new LinkedList();
     LinkedList listaB= new LinkedList();
    /**
     * Creates new form visual
     */
    public visual() {
        t= new hast();
        initComponents();
    }

    /**
     * This method is called from within the constructor to initialize the form.
     * WARNING: Do NOT modify this code. The content of this method is always
     * regenerated by the Form Editor.
     */
    @SuppressWarnings("unchecked")
    //                           
    private void initComponents() {

        jButton1 = new javax.swing.JButton();
        jButton2 = new javax.swing.JButton();
        txt1 = new javax.swing.JTextField();
        txt2 = new javax.swing.JTextField();
        jScrollPane1 = new javax.swing.JScrollPane();
        area1 = new javax.swing.JTextArea();
        B1 = new javax.swing.JButton();
        jButton3 = new javax.swing.JButton();
        jButton4 = new javax.swing.JButton();
        jButton5 = new javax.swing.JButton();
        jButton6 = new javax.swing.JButton();
        jButton7 = new javax.swing.JButton();
        jButton8 = new javax.swing.JButton();

        setDefaultCloseOperation(javax.swing.WindowConstants.EXIT_ON_CLOSE);

        jButton1.setText("añadir elementos A");
        jButton1.addActionListener(new java.awt.event.ActionListener() {
            public void actionPerformed(java.awt.event.ActionEvent evt) {
                jButton1ActionPerformed(evt);
            }
        });

        jButton2.setText("añadir elementos B");
        jButton2.addActionListener(new java.awt.event.ActionListener() {
            public void actionPerformed(java.awt.event.ActionEvent evt) {
                jButton2ActionPerformed(evt);
            }
        });

        area1.setColumns(20);
        area1.setRows(5);
        jScrollPane1.setViewportView(area1);

        B1.setText("AUB");
        B1.addActionListener(new java.awt.event.ActionListener() {
            public void actionPerformed(java.awt.event.ActionEvent evt) {
                B1ActionPerformed(evt);
            }
        });

        jButton3.setText("A/B");
        jButton3.addActionListener(new java.awt.event.ActionListener() {
            public void actionPerformed(java.awt.event.ActionEvent evt) {
                jButton3ActionPerformed(evt);
            }
        });

        jButton4.setText("auto");
        jButton4.addActionListener(new java.awt.event.ActionListener() {
            public void actionPerformed(java.awt.event.ActionEvent evt) {
                jButton4ActionPerformed(evt);
            }
        });

        jButton5.setText("AnB");
        jButton5.addActionListener(new java.awt.event.ActionListener() {
            public void actionPerformed(java.awt.event.ActionEvent evt) {
                jButton5ActionPerformed(evt);
            }
        });

        jButton6.setText("A∁");
        jButton6.addActionListener(new java.awt.event.ActionListener() {
            public void actionPerformed(java.awt.event.ActionEvent evt) {
                jButton6ActionPerformed(evt);
            }
        });

        jButton7.setText("AΔB");
        jButton7.addActionListener(new java.awt.event.ActionListener() {
            public void actionPerformed(java.awt.event.ActionEvent evt) {
                jButton7ActionPerformed(evt);
            }
        });

        jButton8.setText("A ⊆ B");
        jButton8.addActionListener(new java.awt.event.ActionListener() {
            public void actionPerformed(java.awt.event.ActionEvent evt) {
                jButton8ActionPerformed(evt);
            }
        });

        javax.swing.GroupLayout layout = new javax.swing.GroupLayout(getContentPane());
        getContentPane().setLayout(layout);
        layout.setHorizontalGroup(
            layout.createParallelGroup(javax.swing.GroupLayout.Alignment.LEADING)
            .addGroup(layout.createSequentialGroup()
                .addGap(44, 44, 44)
                .addComponent(jScrollPane1, javax.swing.GroupLayout.PREFERRED_SIZE, 265, javax.swing.GroupLayout.PREFERRED_SIZE)
                .addPreferredGap(javax.swing.LayoutStyle.ComponentPlacement.RELATED, javax.swing.GroupLayout.DEFAULT_SIZE, Short.MAX_VALUE)
                .addComponent(jButton4)
                .addGap(25, 25, 25))
            .addGroup(layout.createSequentialGroup()
                .addGap(25, 25, 25)
                .addGroup(layout.createParallelGroup(javax.swing.GroupLayout.Alignment.LEADING, false)
                    .addComponent(jButton1, javax.swing.GroupLayout.DEFAULT_SIZE, 141, Short.MAX_VALUE)
                    .addComponent(txt1))
                .addGap(0, 142, Short.MAX_VALUE)
                .addGroup(layout.createParallelGroup(javax.swing.GroupLayout.Alignment.LEADING, false)
                    .addComponent(jButton2, javax.swing.GroupLayout.DEFAULT_SIZE, 132, Short.MAX_VALUE)
                    .addComponent(txt2))
                .addContainerGap())
            .addGroup(layout.createSequentialGroup()
                .addContainerGap()
                .addGroup(layout.createParallelGroup(javax.swing.GroupLayout.Alignment.LEADING)
                    .addGroup(layout.createSequentialGroup()
                        .addComponent(B1)
                        .addGap(29, 29, 29)
                        .addComponent(jButton3)
                        .addGap(18, 18, 18)
                        .addComponent(jButton5, javax.swing.GroupLayout.PREFERRED_SIZE, 64, javax.swing.GroupLayout.PREFERRED_SIZE)
                        .addGap(32, 32, 32)
                        .addComponent(jButton6, javax.swing.GroupLayout.PREFERRED_SIZE, 67, javax.swing.GroupLayout.PREFERRED_SIZE)
                        .addGap(18, 18, 18)
                        .addComponent(jButton7, javax.swing.GroupLayout.PREFERRED_SIZE, 64, javax.swing.GroupLayout.PREFERRED_SIZE))
                    .addComponent(jButton8))
                .addContainerGap())
        );
        layout.setVerticalGroup(
            layout.createParallelGroup(javax.swing.GroupLayout.Alignment.LEADING)
            .addGroup(layout.createSequentialGroup()
                .addGap(21, 21, 21)
                .addGroup(layout.createParallelGroup(javax.swing.GroupLayout.Alignment.BASELINE)
                    .addComponent(jButton1)
                    .addComponent(jButton2))
                .addPreferredGap(javax.swing.LayoutStyle.ComponentPlacement.RELATED)
                .addGroup(layout.createParallelGroup(javax.swing.GroupLayout.Alignment.BASELINE)
                    .addComponent(txt1, javax.swing.GroupLayout.PREFERRED_SIZE, javax.swing.GroupLayout.DEFAULT_SIZE, javax.swing.GroupLayout.PREFERRED_SIZE)
                    .addComponent(txt2, javax.swing.GroupLayout.PREFERRED_SIZE, javax.swing.GroupLayout.DEFAULT_SIZE, javax.swing.GroupLayout.PREFERRED_SIZE))
                .addGroup(layout.createParallelGroup(javax.swing.GroupLayout.Alignment.LEADING)
                    .addGroup(layout.createSequentialGroup()
                        .addPreferredGap(javax.swing.LayoutStyle.ComponentPlacement.RELATED, 121, Short.MAX_VALUE)
                        .addGroup(layout.createParallelGroup(javax.swing.GroupLayout.Alignment.BASELINE)
                            .addComponent(B1)
                            .addComponent(jButton3)
                            .addComponent(jButton5)
                            .addComponent(jButton6))
                        .addGap(48, 48, 48)
                        .addComponent(jButton8)
                        .addGap(32, 32, 32)
                        .addComponent(jScrollPane1, javax.swing.GroupLayout.PREFERRED_SIZE, javax.swing.GroupLayout.DEFAULT_SIZE, javax.swing.GroupLayout.PREFERRED_SIZE)
                        .addGap(24, 24, 24))
                    .addGroup(layout.createSequentialGroup()
                        .addGap(90, 90, 90)
                        .addComponent(jButton4)
                        .addPreferredGap(javax.swing.LayoutStyle.ComponentPlacement.RELATED)
                        .addComponent(jButton7)
                        .addContainerGap())))
        );

        pack();
    }//                         

    private void jButton1ActionPerformed(java.awt.event.ActionEvent evt) {                                         
        // TODO add your handling code here:
        if(!txt1.getText().equals("")){
       listaA.add(txt1.getText()); 
        }
        area1.setText(String.valueOf("elementos de A"+listaA+"\n"+"elementosd de B"+listaB));
        txt1.setText("");
    }                                        

    private void jButton2ActionPerformed(java.awt.event.ActionEvent evt) {                                         
        // TODO add your handling code here:
        if(!txt2.getText().equals("")){
       listaB.add(txt2.getText()); 
        }
         area1.setText(String.valueOf("elementos de A"+listaA+"\n"+"elementosd de B"+listaB));
         txt2.setText("");
    }                                        

    private void B1ActionPerformed(java.awt.event.ActionEvent evt) {                                   
        // TODO add your handling code here:
  area1.setText(String.valueOf("elementos de A"+listaA+"\n"+"elementosd de B"+listaB+"\n"+t.AUnionB(listaA, listaB)));
    }                                  

    private void jButton3ActionPerformed(java.awt.event.ActionEvent evt) {                                         
        // TODO add your handling code here:
         area1.setText(String.valueOf("elementos de A"+listaA+"\n"+"elementosd de B"+listaB+"\n"+t.AdiferenciaB(listaA, listaB)));
    }                                        

    private void jButton4ActionPerformed(java.awt.event.ActionEvent evt) {                                         
        // TODO add your handling code here:
        listaA.add("8");
        listaA.add("1");
         listaA.add("2");
          listaA.add("3");
           listaA.add("4");
            listaA.add("5");
            
           listaB.add("6"); 
           listaB.add("7"); 
           listaB.add("8"); 
           listaB.add("9");
           listaB.add("1"); 
    }                                        

    private void jButton5ActionPerformed(java.awt.event.ActionEvent evt) {                                         
        // TODO add your handling code here:
      area1.setText(String.valueOf("elementos de A"+listaA+"\n"+"elementosd de B"+listaB+"\n"+t.AinterseccionB(listaA, listaB)));   
    }                                        

    private void jButton6ActionPerformed(java.awt.event.ActionEvent evt) {                                         
        // TODO add your handling code here:
         area1.setText(String.valueOf("se tomo B como universo "+"\n"+"elementos de A"+listaA+"\n"+"elementosd de B"+listaB+"\n"+t.ACOMPLEMENTOUsetomaUcomouniverso(listaA, listaB)));
    }                                        

    private void jButton7ActionPerformed(java.awt.event.ActionEvent evt) {                                         
        // TODO add your handling code here:
         area1.setText(String.valueOf("se tomo B como universo "+"\n"+"elementos de A"+listaA+"\n"+"elementosd de B"+listaB+"\n"+t.AdiferenciasimetricaB(listaA, listaB)));
    }                                        

    private void jButton8ActionPerformed(java.awt.event.ActionEvent evt) {                                         
        // TODO add your handling code here:
             area1.setText(String.valueOf("se tomo B como universo "+"\n"+"elementos de A"+listaA+"\n"+"elementosd de B"+listaB+"\n"+t.AsubconjuntoB(listaA, listaB)));
    }                                        

    /**
     * @param args the command line arguments
     */
    public static void main(String args[]) {
        /*
         * Set the Nimbus look and feel
         */
        //
        /*
         * If Nimbus (introduced in Java SE 6) is not available, stay with the
         * default look and feel. For details see
         * http://download.oracle.com/javase/tutorial/uiswing/lookandfeel/plaf.html
         */
        try {
            for (javax.swing.UIManager.LookAndFeelInfo info : javax.swing.UIManager.getInstalledLookAndFeels()) {
                if ("Nimbus".equals(info.getName())) {
                    javax.swing.UIManager.setLookAndFeel(info.getClassName());
                    break;
                }
            }
        } catch (ClassNotFoundException ex) {
            java.util.logging.Logger.getLogger(visual.class.getName()).log(java.util.logging.Level.SEVERE, null, ex);
        } catch (InstantiationException ex) {
            java.util.logging.Logger.getLogger(visual.class.getName()).log(java.util.logging.Level.SEVERE, null, ex);
        } catch (IllegalAccessException ex) {
            java.util.logging.Logger.getLogger(visual.class.getName()).log(java.util.logging.Level.SEVERE, null, ex);
        } catch (javax.swing.UnsupportedLookAndFeelException ex) {
            java.util.logging.Logger.getLogger(visual.class.getName()).log(java.util.logging.Level.SEVERE, null, ex);
        }
        //

        /*
         * Create and display the form
         */
        java.awt.EventQueue.invokeLater(new Runnable() {

            public void run() {
                new visual().setVisible(true);
            }
        });
    }
    // Variables declaration - do not modify                     
    private javax.swing.JButton B1;
    private javax.swing.JTextArea area1;
    private javax.swing.JButton jButton1;
    private javax.swing.JButton jButton2;
    private javax.swing.JButton jButton3;
    private javax.swing.JButton jButton4;
    private javax.swing.JButton jButton5;
    private javax.swing.JButton jButton6;
    private javax.swing.JButton jButton7;
    private javax.swing.JButton jButton8;
    private javax.swing.JScrollPane jScrollPane1;
    private javax.swing.JTextField txt1;
    private javax.swing.JTextField txt2;
    // End of variables declaration                   
}

y ahora la imagen y listo :