Teaching Mathematics in the Primary Grades
2
SET: INTRODUCTION
Set is a collection/group of well-defined objects
sharing common characteristics. A set is said to be
well-defined if anyone would give exactly the
same members that satisfy the condition. On the
other hand, if the elements may vary due to
perception and opinion, it is not a well-defined set.
Well-defined set NOT well-defined set
Set of students in section Set of energetic students in section
Matapat Matapat
Set of teachers in Grade 7 Set of wise teachers in KHS
Matapat (KHS)
SET: INTRODUCTION
Elements (∈ )- members of the given set.
Example: Set of fingers on a human hand
What are the elements?
thumb
index finger 5
middle finger elements
ring finger
pinky finger ∈
SET: INTRODUCTION
Cardinality or Cardinal Number (n)
– the total number of elements in a given set.
What is the cardinality of a set
containing elements which are Trivia:
primary colors in Philippine Flag? The flag’s
Ans: 3 (n)= 3
length is
Blue, twice its
elements
red width
yellow
SET: INTRODUCTION
Exercises: Given set U which contains prime
numbers less than 10, answer the following;
1.) What are the elements of set U? Prime
Numbers
U = { 2, 3, 5, 7 } are numbers
greater than
2.) What is the n(U) “cardinality of set U”?
one whose
factors are 1
the cardinality of set U is 4 and itself.
SET: INTRODUCTION
Concepts in Studying Set
• capital letters are generally used to name sets
• braces { } are used to enclosed the elements of a set
• commas separate the elements of a set
• an element must be named only once in the listing
• ellipsis … is used to indicate that the list is to
continue indefinitely.
SET: INTRODUCTION
Exercises: Answer the following.
A = { S, A, L, I, S, I } n(A) = 4
What is the cardinality of set A?
Remember
B={RIZAL} n(B) = 1 the use of
What is the cardinality of set B? commas.
SET: INTRODUCTION
The use of ellipsis…
C = { 1, 2, …9 } n(C) = 9
What is the cardinality of set C?
INFINITE SET
set that
contains
n(D) = ∞ limitless/endless
D = { 1, 2, 3, 4,… }
Infinity
What is the cardinality of set D? number of
elements
SET NOTATION
Methods of Writing Set
1.) Roster Method – the set is
described by listing the elements.
Example: A = { Saturday, Sunday }
SET NOTATION
Methods of Writing Set
2.) Set-Builder Notation – short hand used
to write set, often used for set
containing infinite number of elements
Example:
A = { x/x is a day in a week that starts with letter "S"} or
A = { x/x ∈ days in a week that starts with letter"S"}
SUBSET AND UNIVERSAL SET
Universal Set is a set which
contains all elements under
discussion
A set is a subset (⊂) of another
set if every element in this set
is an element of another set.
Set of all Grade 7 Students in KHS
Universal Set
Mapitagan ⊂ Set of all
Mapitagan
subset
Grade 7 students in KHS Matapat
subset
Mapagbigay Masayahin
subset subset
Mapagkumbaba Masikap
subset subset
Masigasig
subset
SUBSET AND UNIVERSAL SET
Remember:
Empty set is a subset of any set
Every set is a subset of itself
Example: List all the subsets of set P
P = { a, b, c } Set P has 8 subsets
3 elements = 8 subsets
No element { }
1 element {a},{b},{c}
2 elements { a, b } , { a, c } , { b, c }
3 elements { a, b, c }
The cardinality of set P is 3.
Using formula 2 n
where n is
the cardinality,
3 elements = 2n
=2 3
=2x2x2
= 8 subsets
APPLICATION: ANSWER THE FOLLOWING
A. State whether the given set is well-defined or not.
n e d s et
e fi
1. The members of your family we l l - d
n e d s e t
l - d e fi
2. The Math teacher in class we l
s e t
d e fi n e d
el l -
3. The set of old people no t w
t
n e d s e
4. The set of all factors of 20 we l l - d e fi
5. The set of all intelligent students in yourset
defi ned
el l -
class no t w
APPLICATION: ANSWER THE FOLLOWING
B. Write the following sets using roster method.
1.) Set B is a set of all factors of 15
B = { 1, 15, 3, 5 }
2.)Set C is a set of the months start with
letter J.
C = { January, June, July}
APPLICATION: ANSWER THE FOLLOWING
C. Given the sets below tell whether the
following statement is Fact or Bluff.
F = { u, n, i, v, e, r, s, a, l } J = { r, u, n } I = { u, n, i, v, e, r, s, i, t, y }
K = { s, i, n } H = { u, n, i, v, e, r, s } L=
{ r, a, i, n } G = { s, u, n }
1.) F ⊂ G BLUFF 4.) L ⊂ H BLUFF
2.) G ⊂ N FACT 5.) F ⊂ T BLUFF
3.) J ⊂ R FACT 6.) K ⊂ L BLUFF
KINDS
OF SET
1.) Empty Set / Null Set
•set with no elements
• { } or Ø used to represent empty or null
set
Example:
A = set of multiples of 9 between
10 and 12
2.) Unit Set
- set with only one element
Example:
B = set of months in a year that starts
with letter “D”
B = {December}
3.) Finite Set
– if the elements of a set can be
counted
Example:
C = set of counting
numbers less than 10
C = { 1,2,3,4,5,6,7,8,9 }
4.) Infinite Set
– does not contain countable
number of elements
Example:
D = counting numbers
D = {1,2,3,4,5…}
5.) Disjoint Sets
– two sets with no elements in
common
Example:
E = { 5, 10, 15}
F = { 20, 25, 30}
Set E and Set F are disjoint sets
6.) Joint Sets
– two sets with common element/s
Example:
G = { 2, 3, 5 }
H = { 4, 5, 6 }
Set G and Set H are joint sets
7.)Equal Sets
– two sets which have exactly the
same elements
Example :
I = { 4, 6, 9 }
J = { 9, 4, 6 }
Set I and Set J are equal sets
8.) Equivalent Sets
- two sets with same cardinality or same
number of elements
Example:
K = { red, blue, pink }
L = {Ana, Elsa, Olap }
Set K and Set L are equivalent
SET OPERATIONS
Set Operation Symbol
Union ∪
Intersection ∩
Difference –
Complement ’
SET OPERATIONS
∪
Union of Sets
it simply refers to the
combination of all the elements
in two or more given sets
SET OPERATIONS
A ∪ B which is read as “A union B”,
elements in A are combined with B.
A = { 2, 3, 5, 7}
B = { 1, 2, 3, 4, 5,}
A ∪ B ={ 1, 2, 3, 4, 5, 7}
SET OPERATIONS
∩
Intersection of Sets
is a set formed by the
common elements of two
or more given sets.
SET OPERATIONS
A ∩ B which is read as “A intersection B”,
elements in A that can be found in B.
A = { 2, 3, 5, 7}
B = { 1, 2, 3, 4, 5,}
A ∩ B = { 2, 3, 5 }
SET OPERATIONS
–
Difference of Two Sets
A – B is set formed by
elements found in set A
but not in set B
SET OPERATIONS
A – B which is read as “A minus B”,
elements found in A but not in B.
A = { 2, 3, 5, 7}
B = { 1, 2, 3, 4, 5 }
A – B = { 7 } B – A = { 1, 4 }
SET OPERATIONS
–
Complement of a Set
Is set of elements found in
the universal set but not in
a given set.
SET OPERATIONS
A’ read as A complement or
complement of set A
U = { x/x counting numbers less than 11}
A = { 2, 3, 5, 7} B = { 1, 2, 3, 4, 5 }
A’ = { 1,4,6,8,9,10 }
B’ = { 6,7,8,9,10 }
APPLICATION:
State whether the
statement is FACT or
BLUFF
•All equivalent sets
are equal sets.
•All unit sets are equivalent
sets.
•All unit sets are finite sets.
State whether
the given set is
finite or
infinite
•Letter of English
alphabet
•Prime numbers
•Teachers in
KHS
State what
kind of set is
being
described
•Set of day in a week that
starts with letter “W”
unit set or finite set
•Set of all people living
on Earth infinite set
•Set of months in a year
with 31 days finite set
•Set of prime numbers
between 19 and 23
Empty set or null set
Given the Universal set U and subsets A, B, C and D
below, write the elements of the ff. set.
U = { x/x is counting numbers less than 10 }
A = { 1, 3, 5, 7, 9 }
B = { 2, 4, 6, 8 }
C = { 2, 3, 5, 7 }
D = { 10 }
Given the Universal set U and subsets A, B, C and D below, write the elements
of the ff. set.
U = { x/x is counting numbers less than 10 }
A = { 1, 3, 5, 7, 9 }
B = { 2, 4, 6, 8 }
C = { 2, 3, 5, 7 }
D = { 10 }
1.) A ∪ B = {1, 2, 3, 4, 5, 6, 7, 8, 9}
2.) B ∩ C = { 2 }
Given the Universal set U and subsets A, B, C and D below, write the elements
of the ff. set.
U = { x/x is counting numbers less than 10 }
A = { 1, 3, 5, 7, 9 }
B = { 2, 4, 6, 8 }
C = { 2, 3, 5, 7 }
D = { 10 }
3.) B – C = { 4, 6, 8 }
4.) B ∩ D = { } or Ø
5.) D’ = {1, 2, 3, 4, 5, 6, 7, 8, 9}
Thank You
God Bless
