SETS--Presentation for Secondary-ppt.ppt

SETS
THE MEANING
OF
HOW DO
WE DEFINE
SETS?
VARIOUS

Show which
woman is the
most beautiful?

A set is a group or collection of
objects
the symbols A={ . . . }

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

is
not a member of
And notated with 

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}

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

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.

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.

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}

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

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

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

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

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.

Pascal Triangle
For the subsets of { }
For the subsets with 1
member
member
member
member

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.

STORY MATTER ABOUT SETS
1.Out of group of 60 children, 50 children like playing basketball, 40 children like
playing badminton, and 35 children like both games.
a. Build a Venn diagram based on the above information!
b. How many children like neither basketball nor badminton?
2. Out of 30 students, 25 students like reading, 20 students like singing, and 4
students like neither reading nor singing.
b. How many children like both reading and singing?
3.From 40 students in the class room, 30 students like mathematics, and 28
students like biology. If 2 students dislike both of lessons, so how many
students who like both of the lessons?
4.Out of a group of persons, 20 persons like soccer, 25 persons like volleyball,
and 18 persons like both games.
b. How many persons are there in that group?

SETS--Presentation for Secondary-ppt.ppt

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