Introduction of Set

1. SETS

2. SETS
THE MEANING
OF SETS
HOW DO
WE DEFINE
SETS?
VARIOUS

3. Objective
•illustrates well-defined sets,
subsets, universal sets, null set, and
cardinality of sets.

4. Show which set of fruits?
Show which set of four-legged animals?

5. Show which
woman is the
most beautiful?

6. What is a sets?

7. Important Terms to Remember
The following are terms that you
1. A set is a well- defined group of objects,
called elements that share a common
characteristic. For example, 3 of the objects
above belong to the set of head covering or
simply hats (ladies hat, baseball cap, hard
hat).

8. 2. The set F is a subset of set A if all
elements of F are also elements of A.
For example, the even numbers 2, 4 and
12 all belong to the set of whole
numbers. Therefore, the even numbers
2, 4, and 12 form a subset of the set of
whole numbers. F is a proper subset
of A if F does not contain all elements
of A.

9. •3. The universal set U is the set
that contains all objects under
consideration.
•4. The null set Ǿ is an empty set.
The null set is a subset of any set.
•5. The cardinality of a set A is
the number of elements contained
in A.

10. Notations and Symbols
In this section, you will learn some of the
notations and symbols pertaining to sets.
1. Uppercase letters will be used to name
sets and lowercase letters will be used to
refer to any element of a set. For
example, let H be the set of all objects
that cover or protect the head. We write
H = {ladies hat, baseball cap, hard hat}

11. •2. The symbol Ǿ or { } will be used to
refer to an empty set.
•3. If F is a subset of A, then we write F Í
A. We also say that A contains the
•set F and write it as A Ê F . If F is a
proper subset of A, then we write F Ì A.
•4. The cardinality of a set A is written as
n(A).

12. what is the relation
with

13. is
elements or members of
In set language, the Greek letter
epsilon means “is a
members or elements of ”


14. is
not a member of
And notated with

15. 

16. How to Define a sets
• Describing the elements
A = {whole number from 1 until 6}
• Listing the elements
A = {1, 2, 3, 4, 5}
• Set Notation
A = {x | x < 6, x ЄA}

17. NUMBER OF ELEMENTS IN A SET
Usually, for a sets we denote the number of
elements in A as n(A)
Example:
Given A = {Odd number between 10 and 26}.
Find the number of element A!
Solution:
A = {11, 13, 15, 17, 19, 21, 23, 25}
The number of element A is n(A) = 8

18. VENN DIAGRAM
In a class there are30 students. They are
having a discussion. They are divided
into 6 groups (A, B, C, D, E, and F)
consisting of 5 people.

19. E F
B
D
A C
Venn
diagram
The rectangle is the set that contains all
the sets in discussion. It is called the
universal set.

20. S A
1

3

5

7

2

4

Find the universal sets of the venn diagram?
S = {1, 2, 3, 4, 5, 7}
Find the sets of A?
A = {1, 3, 5, 7}

21. EQUIVALENT SETS
S = {x:x is the first 5 natural
numbers or x is vocal of alphabet}
A = { 1,2,3,4,5}  n(A) = 5
B = { a,i,u,e,o}  n(B) = 5
S A~B
A
5
B
5

22. SUBSETS
B
A 
A
B 
Is read “A is the subset of B”
Is read “B contains A”
Let:
S = {1, 2, 3, 4, 5, 6, 7}
P = {1, 2, 3, 4, 5, 6}
Q = {2, 4, 6}
Determine the relationship
between the set P and the
set Q!
S
.2
.4 .6
.1
,3
.5
.7

23. n Himpunan Himpunan Bagian Jumlah
0  
1 {a}  , {a}
2 {a, b}  , {a} , {b}, {a, b}
3 {a, b, c}  , {a}, {b} , {c},{a, b} ,{a, c},
{b, c} , {a, b, c}
1
2
4
8
4
1 =
2 =
4 =
8 =
.
.
.
2k
? ? ?
5 ? ? ?
:
. :
. :
. :
.
k
20
21
22
23
Finding All Subsets and The Number of Subsets of a Set

24. EXAMPLE 1:
Find all possible subsets of {a, b}!
Answer:
Possible subsets of {a, b, c} are:
{ } has no member
{a}, {b} has 1 member
{a, b} has 2 member

25. Example 2:
Find the number of all possible subsets of B = {a, b, c}!
Answer:
B = {a, b, c}, so n(B) = 3
Number of all possible subsets of B is = = 8
3
2
Find the number of all possible subsets of D = {1, 2, 3, 4,
5, 6}!
Answer:
n(D) = 6
So, number of all possible subsets of D is 26 = 64.

26. Pascal Triangle
For the subsets of { }
For the subsets with 1
member
For the subsets with 2
member
For the subsets with 3
member
For the subsets with 4
member

27. Example:
Find the number of subsets of A = {p, i, z, a} which have 2 member!
Answer:
The number of subsets which have 2 members
is 6.
Example:
Find the number of subsets of B = {xI 2 < x < 10, x is a whole number}
which have 5 member!
Answer:
The number of subsets which have 5 members
is 56.

28. Do the following exercises.
1. Give 3 examples of well-defined
sets.
2. Name two subsets of the set of
whole numbers using both the listing
method and the rule method.
3. Let B = [1, 3, 5, 7, 9}. List all the
possible subsets of B.
4. Answer this question: How many
subsets does a set of n elements
have?

29. Draw a Venn diagram to show the
relationships between the following pairs
or groups of sets:
1. E = {2, 4, 8, 16, 32}
F = {2, 32}
2. V is the set of all odd numbers
W = {5, 15, 25, 35, 45, 55…}
3. R = {x| x is
a factor of 24}
S = { }
T = {7, 9, 11}

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