Highlights
Objectives:
Practice java programming with classes and objects, constructors, copy constructors, enum type, array, ArrayList (generic version), overloaded methods, passing by reference etc.
Task
In mathematics, a set is a collection of distinct elements and elements in a set are not in order. Here are some examples of sets:
(a) A set of integers, e.g. integerSet = {3, 1, 4, 2}
(b) A set of fruits, e.g. fruitSet = {apple, orange, papaya}
(c) A set of characters, e.g. charSet = {‘A’, ‘m’, ‘&’}
We always enclose elements of sets inside a pair of { }.
Here are some other properties on sets:
(1) A set can be empty, i.e. no element. We call it empty set. In mathematics, we have a special symbol to denote empty set. Convenient to our design later, we will use { } to denote an empty set.
(2) When checking an element is inside a set. We call it “belong to”.
(3) If a set contains in another set, we call it subset. For example, {1, 2, 3} is a subset of {2, 3, 4, 6, 1}. Therefore, empty set is a subset of every set.
(4) The cardinal number of a set is the number of elements in a set.
(5) The union of two sets A and B are all the elements belong to A and B, minus the duplications. For example, if A = {1, 2, 3} and B = {2, 3, 4, 5}, the union is {1, 2, 3, 4, 5}.
(6) The intersection of two sets A and B are the common elements of A and B. Using the example quoted in (5), the intersection is {2, 3}.
(7) The equality of two sets A and B are all the elements of A are in B and all the elements of B are in A. Or alternatively, A is the subset of B and vice versa.
(8) The difference of two sets A and B, for example A – B, is those elements in B should not be in A. For example, if A = {1, 2, 3} and B = {2, 3, 4, 5}, A – B = {1} and B – A = {4, 5}.
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