Thread: Set Class

I'm having trouble implementing a few methods in a class I have to make. The class deals with the operations of sets. Like union of two sets and intersection of two sets. Yes I know there is already a Set class, but I am having to implement my own. I seem to be having trouble with the symDiff (Symmetric Difference) , diff (Difference), and others.

package setApp;
 
import java.util.*;
 
public class Set
{
   private ArrayList<String> elements;
 
   /**
    * creates an empty set
    */
   public Set()
   {
       elements = null;
   }
 
   /**
    * creates a set using the elements of the ArrayList s.
    * @param s the ArrayList whose elements are used to
    *        create this set.
    * @throws IllegalArgumentException if s contains duplicity.
    */
   public Set(ArrayList<String> s)
   {
       int i;
       elements = new ArrayList<String>();
       for(i=0; i<s.size(); i++)
       {
          if (elements.contains(s.get(i)))
              throw new IllegalArgumentException("Set(ArrayList<String>):duplicity not allowed in sets");
          elements.add(s.get(i));
       }
   }
 
    /**
    * creates a set using the elements of the array s.
    * @param s the array whose elements are used to
    *        create this set.
    * @throws IllegalArgumentException if s contains duplicity.
    */
   public Set(String[] s)
   {
       int i;
       elements = new ArrayList<String>();
       for(i=0; i<s.length; i++)
       {
          if (elements.contains(s[i]))
              throw new IllegalArgumentException("Set(String[]):duplicity not allowed in sets");
          elements.add(s[i]);
       }
   }
 
   /**
    * determines whether a set contains the specified element
    * @param elt an element
    * @return true if elt is an element of this set; otherwise, false
    */
   public boolean isElement(String elt)
   {
       return elements.contains(elt);
   }
 
   /**
    * determines the size of this set.
    * @return the size of this set.
    */
   public int cardinality()
   {
       return elements.size();
   }
 
   /**
    * computes the intersection of this set and the
    * specified set.
    * @param s a set
    * @return a set representing the intersection of this set
    *         and s.
    */
   public Set intersect(Set s)
   {
       int i;
       ArrayList<String> result = new ArrayList<String>();
       for (i=0;i<s.cardinality();i++)
           if (this.isElement(s.elements.get(i)))
               result.add(s.elements.get(i));
       return new Set(result);           
   }
 
   /**
    * computes the union of this set and the specified set.
    * @param s a sets
    * @return a set representing the union of this set
    *         and s.
    */
   public Set union(Set s)
   {
          int i;
          ArrayList<String> result = new ArrayList<String>();
          for (i=0; i<s.cardinality(); i++) 
          {
        	  if (elements.contains(i))
        		  result.add(s.elements.get(i));  		  
          }
          return new Set(result);
   }
 
   /**
    * computes the difference between this set and the
    * specified set.
    * @param s a set
    * @return a set representing the difference between
    *         this set and s.
    */
   public Set diff(Set s)
   {
 
 
   }
 
   /**
    * computes the symmetric difference between this set
    * and the specified set.
    * @param s a set
    * @return a set representing the symmetrix difference
    *         between this set and s.
    */
   public Set symDiff(Set s)
   {
       //implement this method     
   }
 
   /**
    * computes the Cartesian product for this set
    * and the specified set.
    * @param s a set
    * @return a set representing the Cartesian product
    *         of this set and s.
    */
   public Set xProduct(Set s)
   {
       //implement this method
   }
 
 
   /**
    * determines whether a set is empty
    * @return true if this set is empty; otherwise, false
    */
   public boolean isEmpty()
   {
       return elements.isEmpty();
   }
 
   /**
    * determines whether this set is equal to the specified
    * set.
    * @param s a set
    * @return true if this set is equal to s; otherwise, false
    */
   public boolean equals(Set s)
   {
       //implement this method
   }
 
   /**
    * determines whether this set is a subset of the specified set.
    * @param s a set
    * @return true if this set is a subset of s; otherwise, false
    */
   public boolean subset(Set s)
   {
       //implement this method
 
   }
 
   /**
    * determines whether this set is a proper subset of the specified set.
    * @param s a set
    * @return true if this set is a proper subset of s; otherwise, false
    */
   public boolean properSubset(Set s)
   {
       //implement this method
   }
 
   /**
    * returns a string {x1,x2,...,xn} representing this set,
    * where x1,x2,...,xn are elements of this set.
    * @return a string representation of this set formatted
    *         as specified.
    */
   public String toString()
   {
       //implement this method            
   }   
}