Notesale: Turn your study into money

Document Preview

Extracts from the notes are below, to see the PDF you'll receive please use the links above

---

SETS: AN INTRODUCTION
(Set, Subset, Cardinality of Set, 3 Ways of Describing a Set, Equal and Equivalent Sets, Types of Set)

Name: _____________________________

In this lesson, you are expected to:
 Define and illustrate well-defined sets, subsets, universal sets, null set, cardinality of sets
...
SET
1
...
Each object in a set is called a member or an element of a set
...

2
...

Example
...
1 Sort the following objects into the following sets: fruits(A), flowers(B)
Rose, banana, gumamela, apple, jasmine, orchid, grape, mango
Solution: A = {banana, apple, grape, mango}
B= {rose, gumamela, jasmine, orchid}
Set
Element (∈) read as “is an element of” or “Is a member of” Cardinality
A = { banana,apple, grape, mango,}
n(A) = 4
Banana ∈ A read as Banana is an element of A
Apple ∈ A
read as apple is a member of A
Grape ∈ A
read as grape a member of A
mango∈ A
read as mango is an element of A
If an element, say rose does not belong to set A, then we write rose∉ A, where the ∉ is the sign which means “is not
an element of” or “is not a member of”
Example 1
...
What are the elements of set X? the elements are a, e, i, o, u
...

2
...

3
...

⊆ = read as “ is a subset of”
⊈ = read as “ is not a subset of”
SET
Subset (⊆)?
Y= {0,1,2,3,4,5,6,7,8,9,10} X= {0,2,4,6,8}
Z= {1,2,3,4,5}
Q= {3,6,9,12}

Explanation
X ⊆ Y because every element of X is an element of Y
...

Q ⊈ Y because 12 ∉ Y

Equal Sets, Equivalent Sets
Equal Sets
Equivalent
Set

Definition
- contain exactly same elements and
the number of elements are the same
- contains same number of elements
but the elements may differ

Examples
1
...
X= {a, b, c, d, e, f} and Y= {a, f, b, e, c, d}, then X= Y
1
...

2
...


Types of Set
FINITE SETS- number of elements can be
counted
INFINITE SETS- number of elements cannot be
counted
SINGLETON SET- exactly one element
EMPTY SET/ NULL SET - contains no element
...

UNIVERSAL SET- set containing all elements of
interest in a particular situation
...


Examples
A = { banana, apple, grape, mango}
B = {2,4,6,8,…, 100}
A = {2,4,6,8,…}
The set of natural numbers
{8} is a single ton set, containing only one element
The current vice president of the Philippines
The set of months having more than 31 days
The set of number of days in a year having 400 days
...


Ellipses -if a set
contains many
elements, three
dots called
ellipses are used
to indicate that
the list continues
in the same
manner
...


Universal set example
1
...
If A= {5, 10, 15, 20,…} , B ={10, 20, 30, 40, 50,…}, C={3, 6, 9,12,…}, what is the universal set?
U = {3, 5, 6, 9, 10, 12, 15, 20, 30, 40, 50,…}

Activity 1
Directions: Read and answer the questions carefully
...

_____ 1
...
The set of big people
...
The set of prime numbers
...
The set of happy people
...
The set of intelligent teachers
...
Which of the following is a FINITE set?
A
...
}
C
...

B
...
Set of fractions between 1 and 12
...
Which of the following pairs of sets given below are equal?
A
...
W = {grapes, apples, oranges}
Z = {7, 9, 10}
X = {grapes, peaches, apples, oranges}
B
...
R is the set of letters in the world bank
...

_____ 4
...

A
...
{o, a, y}
C
...
{m, o, n, d, a, y}
_____ 5
...
5
B
...
7
D
...
How will you express the given set below in the verbal method?
M = {January, June, July}
A
...

B
...

C
...

D
...

_____ 7
...
Y = {a, b, c}
C
...
T = {algebra, geometry, trigonometry}
D
...

V = {geometry, trigonometry, algebra}
S is the set of letters in the word post
...
If F = {1,3, 5, 7, 9, 11, 13 }, then which of the following is a subset of F?
A
...
{2, 4}
C
...
{1, 9, 5, 13}
_____ 9
...
Quadrilateral ⊆ Polygon
C
...
Even Numbers ⊆ Odd Numbers
D
...
What does the given statement below mean?
K={}
A
...

C
...

B
...
Set K contains all the elements under consideration
...
What is the cardinality of A = { 5, 6, 3, 2, 3 }?
A
...
4
C
...
6
_____ 12
...
{2, 3, 5, 7}
B
...
{2, 3, 5, 7, 9}
D
...
If M represents the set of even numbers, then which of the following is CORRECT?
A
...
200 ∉ M
C
...
{2, 4, 5 } ⊂ M

Activity 2
Fill in the table below with the correct translation of the given description of sets
...


2
...


3
...


5
...
Give at least 3 examples of set in our life
...


...

2
...
Luisa V
...
Muoas, Josephine L
...
T

---