Set-theoretical Operations

In Mathematics, two sets can be "added" together. Thus, for example, the union of $A$ and $B$, denoted by $A \cup B$, is the set of all elements of either $A$ or $B$.

We can include this operation in the Set ADT:

/**
 * Constructing a new set with elements that are in this set or
 * in the other set.
 *
 * @param other set.
 * @return all elements that are in this set or the other set.
 */
Set<T> union(Set<T> other);

The intersection of $A$ and $B$, denoted by $A \cap B$, is the set of elements that are members of both $A$ and $B$.

/**
 * Constructing a new set with elements that are in this set and
 * in the other set.
 *
 * @param other set.
 * @return the elements this set and other set have in common.
 */
Set<T> intersect(Set<T> other);

The set difference of $A$ and $B$, denoted by $A - B$, is the set of all elements that are in $A$ but not in $B$.

/**
 * Constructing a new set with elements that are in this set but not
 * in the other set.
 *
 * @param other set.
 * @return the elements in this set but not in the other set.
 */
Set<T> subtract(Set<T> other);

These operations can be defined for OrderedSet ADT as well:

OrderedSet<T> union(OrderedSet<T> other); 
OrderedSet<T> intersect(OrderedSet<T> other);  
OrderedSet<T> subtract(OrderedSet<T> other);  

We leave it to you as a challenge exercise to implement these operations efficiently.