VI. Operation of Set (continuation)

3. Difference of two sets.
If A and B two sets, then we can form a new set of elements consisting of members of set A is not a member of set B. This new set of written A - B, and read "set A less set B"; or if it is written with a set-forming notation : A - B = {x | x ∈ A and x ∉ B}.
Formed a new set of elements may also be a member of set B are not members of set A, and it is written as B - A, read as "less a set A set B"; or if it is written with a set-forming notation: B-A = {x | x ∈ B and x ∉ A}.

For example:
If A = {1, 2, 3, 4, 5, 6, 7} and B = {1, 3, 5}, then A - B = {2, 4, 6, 7}
If A = {a, b, c} and B = {a, b, c, d, e, f}, then B - A = {d, e, f}
If C = {3, 5, 7} and D = {3, 5, 7}, then A-B = {} or A - B the set is empty.

4. The set of the same Set.

Two sets A and B is said to equal if and only if every member of A is a member of B as well, or vice versa, every member of B is a member of A as well.
Two sets A and B are the same written A = B, or if written with a set forming notation set : A = B = {x | x ∈ A and x ∈ B}.
For example:
If A = {2, 3, 1, 5, 4} and B = {1, 2, 3, 4, 5}, then A = B.
If A = {b, c, d} and B = {b, c, d}, then A = B.
Note that the order of the writing member is not a problem on any set (not shown differences in membership of a set).

VII. OPERATION of SET (continuation).

2. Combined sets.

Of the two sets P and Q we can establish a new set of C whose membership consists of the elements of P and Q. The set K is called set combination of P and Q. The set combination is written: K = P ∪ Q, reads: The set of K equal to the combined P Q or set of K equal to the combined P and Q. When written in a way "set shaper": K = {x | x ∈ P or x ∈ Q}.

For example:
a. If A = {p, q, r} and B = {k, l, m, n, o, p, q, r}, then A ∪ B = {p, q, r, k, l, m, n , o}

b. If C = {-1, 0, 1, 2, 3, 4, 6} and D = {0, 2, 4, 6}, then C ∪ D = {-1, 0, 1, 2, 3, 4 , 6}

c. If K = {the boys Mr. Amir} and L = {girls pack Amir
then K ∪ L = {children} pack Amir

d. If P = {2, 3, 5, 7,} and P = {2, 3, 5, 7}, then P ∪ Q = {2, 3, 5, 7,}

The examples above, if drawn with a Venn diagram:
Fig. 5.

III. HOW TO REPRESENT AN ELEMENT / MEMBER OF SET

How do I write or declare an object or something as a member / element of a specific set?
To say "member" of a set of used notation "∈". To say "not a member" used the notation "∉".
For example:

If A = {2, 3, 5, 7, 11}, then:
2 contained in A, means that 2 members of A and written 2 ∈ A
7 contained in A, means the 7 members of A and written 7 ∈ A
1 is not contained in A, means 1 is not a member of A and written 1 ∉ A
6 is not contained in A, means that 6 is not a member of A and written 6 ∉ A
etc.

IV. ELEMENTS OF A SET OF NUMBER PASSED
To state the amount or number of members of the set used the notation "n (name set)"
For example:
A = {chicken, ducks, goats, cows}, the number of members of A = 4, and write n (A) = 4.
B = {2, 4, 6, 8, 10}, the number of members of B = 5, and is written n (B) = 5.

II. HOW TO REPRESENT A SET OF

As a symbol of a set of use curly braces {...}. Statements about members of the set were written between curly braces open and close it.

To distinguish a set with another set, a set is usually expressed (given name) with an uppercase (capital), for example: A, B, C, D,. . . , Or Z.

How do I declare or write a Set ?

There are 4 (four) way of writing to express a set:

1. By way of registering or tabulation, in particular by mentioning / write members one by one. Writing members to each other separated by a comma.

1.a. For a set with members of the limited and small. Members of the set is written all one by one.
For example:
A = {-1, -2, -3, -4, -5}
B = {January, February, March, April}

1.b. For the set with a limited member but many. Members may not be listed all. Its members are listed some of course, continue with 3 points. . . , (Mean / read and so on) and then ends with the last member.
For example:
C = {1, 2, 3, 4, 5,. . . , 69}
D = {a, b, c, d, e,. . . , z}

1.c. For sets with many members and is not limited. Members of the set is represented by some only, at least 4, and for other members who are not mentioned enough to be represented by 3 points. . . , Which means and so on.
For example:
E = {1, 2, 3, 4,. . . }
F = {Bandung, Jakarta, Semarang, Bogor. . . . }

2. Description formula, namely with mention membership requirements.
For example:
Example in 1.a above, if written in a description formula:
A = { negative interger between 0 and -6}
B = {name of first 4 months of the year AD}

3. By writing the member notation of the set.

3.a. Every object or object member is represented by a set of variables.
For example:
The set B above when written this way to be B = {a, b, c, d}. So, a representative of January, b represents February, March and d c represents a representing March.

3.b. All members of the set denoted by a notation and write "membership requirements" behind the sign "|".
For example:
If the sample 1.a. above was written this way to be:
A = {x | 0> x> - 6, x integer}
B = {x | x = name of the first 4 months of the year AD}

4. With Picture of sets. Venn Diagran
For example: Venn diagram of A = {1, 2, 3, 4, 5, 6}
Fig. 1.

A. SET CONCEPT

1. UNDERSTANDING
An understanding of the set is one of the important and fundamental concepts in modern mathematics. The concept of the set was first introduced officially by a German mathematician Georg Cantor in the 19th century.

The concept of the set is found, explicitly or implicitly, in every field of pure and applied mathematics. Explicitly, the principles and terminology set used to make the statement more clear and precise mathematics and to explain concepts such as limited and unlimited.

What is the set?

SET is a collection of objects or anything else that is clearly defined so that we can easily find out whether an object or something else was included in a set or not.

The objects or other things that are included in a set called members or elements of the set or collection of these.
If someone says: "Above the dining table is a stack of notebooks." So we can imagine that on the dining table was a stack of notebooks, in the pile notebook only, not other objects, papers or other.

In a sentence on a stack is a set and a member or set of elements that are writing books, writing books and not just reading books or other objects.
In the set of the above a member conditions are notebooks are piled on the dining table, and from the membership requirement is to clearly know where the objects belonging to members of the set which do not include members of the set.

So it is clear to create a Set, the membership requirements of the members or elements of a set that will be formed must be presented clearly so that for any set anyone can tell whether an object or certain other things that are members of the set or not.

Terms or the nature of the set of member characteristics on a set. Characteristic is what distinguishes a set with another set. These characteristics are also useful for giving a name to a set.

Another example:
The set of integers. Here the member characteristics / requirements of a set are integers.
Association of European countries. Here the member requirements / characteristics are the countries in continental Europe
Etc..