Add the methods union , intersection , and difference to the class Array Bag . Exercises 6, 7, and 8 of Chapter 1 describe these operations.

Exercises 6:

The union of two bags is a new bag containing the combined contents of the original two bags. Design and specify a method union for the ADT bag that returns as a new bag the union of the bag receiving the call to the method and the bag that is the method's one argument. Include suffi cient comments to fully specify the method. Note that the union of two bags might contain duplicate items. For example, if object x occurs fi ve times in one bag and twice in another, the union of these bags contains x seven times. Specifically, suppose that bag1 and bag2 are bags; bag1 contains the strings a , b , and c ; and bag2 contains the strings b , b , d , and e . The expression bag1 .union(bag2) returns a bag containing the strings a , b , b , b , c , d , and e . Note that union does not affect the contents of bag1 and bag2.

Exercises 7:

The intersection of two bags is a new bag containing the entries that occur in both of the original two bags. Design and specify a method intersection for the ADT bag that returns as a new bag the intersection of the bag receiving the call to the method and the bag that is the method's one argument. Include sufficient comments to fully specify the method. Note that the intersection of two bags might contain duplicate items. For example, if object x occurs five times in one bag and twice in another, the intersection of these bags contains x two times. Specifically, suppose that bag1 and bag2 are bags; bag1 contains the strings a , b , and c ; and bag2 contains the strings b , b , d , and e . The expression bag1 .intersection(bag2) returns a bag containing only the string b . Note that intersection does not affect the contents of bag1 and bag2

Exercises 8:

The difference of two bags is a new bag containing the entries that would be left in one bag after removing those that also occur in the second. Design and specify a method difference for the ADT bag that returns as a new bag the difference of the bag receiving the call to the method and the bag that is the method's one argument. Include sufficient comments to fully specify the method. Note that the difference of two bags might contain duplicate items. For example, if object x occurs fi ve times in one bag and twice in another, the difference of these bags contains x three times. Specifi cally, suppose that bag1 and bag2 are bags; bag1 contains the strings a , b , and c ; and bag2 contains the strings b , b , d , and e . The expression bag1.difference(bag2) returns a bag containing only the strings a and c . Note that difference does not affect the contents of bag1 and bag2.