set : the subset
SET
: THE SUBSET
I.
DEFENITION
OF THE SET
The set is a collection of objects or element of a
kind clearly , so that the object can be determined precisely which includes
the set and which are not included in the set. The meaning is clearly defined can
be determined unequivocally object or any object that is included and not
included in a set are known. Objects that are included in the set are called members,
object, or elements of a set. For further used the term member or element. Based
on the above definition, it is a collection or group of objects or object is not
necessarily a set.
Example of Set :
· A
= {Set of students majoring in mathematics education University of Muhammadiyah
Makassar}.
· B
= {The set of children aged under 10 years}.
Example of not Set :
· Set
of beautiful girls.
· Set
of long-haired men.
II.
SUBSET
To understand the definition of subsets, consider
the following example :
Let B be the set of
students at your school and set A is the set of students in your class . Of the
two sets can be seen that all the members of set A are members of set B.
Relationship between A and B is called a subset . In general , the subsets are
defined as follows .
“The
set A is a subset of set B if and only if every element of A is an element of B”.
Notation : A B or A ⊂
B.
Consider the following example .
From the diagram above,
given the set A = { a, b, c} and set B = { a, b, c, d, e } . Set A = { a, b, c
} is a subset of the set B = { a, b, c, d, e } for all the set A , ie 1 and 2
is in the set B. A set is a subset of B and is written A Ì
B.
For any set A apply the following matters :
1) A is a subset of A itself
(ie, A A).
2) The empty set is a
subset of A ( A).
3) If A Í
B and B Í
C, then A Í
C
- A and A Í A, then and A is called the set of real part (improper subset) of the set A.
- A Í B and B is different from A Ì B.
- A Ì B: A is a subset of B but A ¹ B. A fact is a subset (proper subset) of B. Example: {1} and {2, 3} is a proper subset of {1, 2, 3}
- A Í B: used to indicate that A is a subset (subset) of B that allows A = B. Example: A = {1, 2, 3}, then {1, 2, 3} and Æ is improper subset of A.
III.
NUMBERS
OF SUBSET
To determine the number of subsets of a set to
consider the following table :
|
SET
|
NUMBERS OF SET
|
SUBSET
|
NUMBERS OF SUBSET
|
|
A= {1}
|
N (A) = 1
|
{ }, {1}
|
2 = 21
|
|
A= {1, 2}
|
N (A) = 2
|
{ }, {1}, {2}, {1,2}
|
4 = 22
|
|
A= {1, 2, 3}
|
N (A) = 3
|
{ }, {1}, {2}, {3}, {1, 2}, {1, 3}, {2,3}, {1, 2,
3}
|
8 = 23
|
|
A= {1,2,3,…}
|
N (A) = n
|
{ }, {1}, {2}, {3,}, ….
{1, 2, 3,…}
|
2n
|
Refers to table above, appears that there is
relationship about numbers of set and the numbers of subset the set. Thus, can
be concluded : the numbers of subset from the set is 2n, when n is the numbers
of set.
Example :
- Fill in the blanks below with the notation Í or Ì .
a.{1, 2} ... {1,
2}
b.{1, 2} ... {1, 2, 3}
c.{3, 4, 5} ...
{3, 4, 5}
d. {4} ... {4, 5, 6 }
Answer :
a. {1, 2} Í
{1, 2}
b. {1, 2} Ì
{1, 2, 3}
c. {3, 4, 5} Í
{3, 4, 5}
d. {4} Ì
{4, 5, 6}
2. Given the set K = {the
letters making up the word "MANTAN"}
a. Define a
subset of K which has two members.
b. Define a subset of K
which has three members.
c. Define a
subset of K which has four members.
Answer:
K = {the
letters making up the word "MANTAN"}
= {M, A, N, T, A, N}
a. Subsets of K which
has two members is {M, A}, {M, N}, {M, T}, {A, N}, {A, T}, {N, T}.
b. Subsets of K which has
three members is {M, A, N}, {M, N, T}, {M, A, T}, {A, N, T}.
c. Subsets of K which
has four members is {M, A, N, T}.
REFERENCES
Cholik A, M. 2004. Matematika Untuk SMP/MTs VII .Jakarta
: Erlangga
Wagio, A. 2008. Pegangan Belajar Matematika SMP/MTS
VII. Jakarta : Depdiknas
Wiranti, Atik. 2008. Contextual Teaching and
Learning Matematika SMP/MTS 1.
Jakarta : Depdiknas
http://id.wikipedia.org/wiki/Himpunan_(matematika)
http://www.google.com/url?q=http://file.upi.edu/Direktori/FPMIPA/JUR._PEND._MATEMATIKA/
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