Ppt sets and set operations

Mr. Gerald DG Banaag
Elizabeth Seton School

How do we know when an object is
intrinsically part of a set or not? Why do
we have to consider objects as such?
Why do you think the study of the
concept of sets important?
How is the concept of sets being used in
other fields of study?
Which is more essential: the learning of
the concept of sets or the acquisition of
knowledge of the set of real numbers?

KWLH Chart
 Describe and illustrate well-defined sets,
subsets, universal set, and null set.
 Define and describe the union and
intersection of sets and the complement of a
set.
 Use Venn diagram to represent sets, subsets,
and set operations.
 Explain the concept of Venn diagram.
 Create a Venn diagram of elements classified
in different sets.
 Solve problems involving sets.

 Personality Development
1. Why do we have to consider ourselves as part of a
group?
2. Is it possible for someone to be part of more than
one group?
3. Is it beneficial to be part of any group?
4. How did you relate the lessons with your personal
experiences as a teenager?
5. How do you think these lessons will affect your
personality and outlook in life?
 Learning Process
1. How did you learn the lesson on sets?
2. Which part of the lesson struck you the most?
Why?

 Identify the object that does not belong to the
group.
a. boat, kalesa, car, bus, airplane
b. carabao, chicken, cow, pig, goat
c. Camiguin, Bukidnon, Basilan, Cebu, Davao del Sur
d. hexagon, quadrilateral, rectangle, rhombus,
square
e. 2, 12, 24, 11, 30

 How do you know when an object does not
belong to a group?
 How do we know if a group is considered a set?
 How do you identify objects that belong to a
particular group?
 What is your intuitive concept of a set?
 What do you call objects that belong to a given
set?
 Can you give everyday experiences that use the
concept of sets?
 What is the main characteristic of a set in
Mathematics?

¤ A group or collection of well-defined distinct
objects is called a __________.
When do we say that a
collection is “well-defined”?
set
When do we say that an
object belongs to a group?
¤ Each object in a set is called a __________
or an __________ of a set.
member
element

 Determine whether the following is a set or not:
1. The collection of all ESS teachers.
2. Tall students in Grade 7.
3. Rich people in the Philippines.
4. Planets in the Solar System.
5. Beautiful girls in the class.
6. People living on the moon.
7. The collection of all large numbers.
8. The set of all multiples of 5.
9. A group of good writers.
10. Nice people in your class.

“Racism is man’s gravest threat to man - the
maximum of hatred for a minimum reason”
Abraham J. Heschel
(Jewish theologian and philosopher)
“At the heart of racism is the religious assertion
that God made a creative mistake when He
brought some people into being”
Friedrich Otto Hertz

 Can you provide possible members of the
following groups, if possible?
a. Students over 12 years old in the class.
b. Counting numbers less than 5.
c. Set of letters in the word Philippines.
d. Prime numbers which are even.
e. Handsome boys in the class.

How do you define the terms contained
in a set?
When do we know if a set if null or
empty?
Why do we have to identify whether a
set is finite or infinite?
How do you think these terms can be
presented?

 The Roster Notation or Listing Method
This is a method of describing a set by listing
each element of the set inside the symbol { }. In
listing the elements of the set, each distinct
elements is listed once and the order of the
elements does not matter.
ex. Colors of the rainbow
R = {red, orange, yellow, green, blue, indigo, violet}
[List the elements in Exploration # 2]

 The Set Builder Notation
It is a method that lists the rules that
determine whether an object is an element of the
set rather than the actual elements.
ex. All cities in the Philippines
A = {x| x is a city in the Philippines}
read as:
“A is the set of all x such that x is a city in the
Philippines.”

 Describe the following sets using the specified
methods.
A. Write a verbal description for each of the
following sets:
1. D = {1, 3, 5, 7, . . . }
2. E = {a, b, c, . . . , z}
3. F = {4, 8, 12, 16, . . . , 96}
Answer:
1. The set of odd numbers.
2. The set of small letters in the English
alphabet.
3. The set of multiples of 4 between 0 and 100.

methods.
B. List the elements of the following sets:
1. M = {x|x > 7, x is an odd integer}
2. A = {x|7 < x < 8, x is a counting number}
3. T = {x|x is a city in Metro Manila}
4. H = {x|x is a counting number between 7 and 10}
Answers:
1. M = {9, 11, 13, 15, 17, . . . }
2. A = { } or 
3. T = {Manila, Caloocan, Las Piñas, . . . Pasig}
4. H = {8, 9}

methods.
C. Write a rule for the following:
1. S = {a, e, i, o, u}
2. E = {3, 6, 9, . . . , 30}
3. T = {Monday, Tuesday, Wednesday, . . . , Sunday}
Answers:
1. S = {x  x is a vowel in the English alphabet}
2. E = {x  3  x  30, x is a multiple of 3}
3. T = {x  x is a day in week}

Can you share to the class some
new terms you learned today?
Which definition struck you the
most?
If you can share a topic that you
learned today to a friend, what
would it be? Why?

 Bring a photo of your favorite actors
 Define the following:
1. Equal
2. Equivalent
3. cardinality of a set
4. Universal Sets
5. Subsets

Ppt sets and set operations

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Ppt sets and set operations