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Reference:
Nivera, G. C. (2013), Grade 7 Mathematics: Pattern and Practicalities. Don Bosco Press Inc. Makati City, Philippines.
This will help you in illustrating operations on sets using Venn Diagram. Also, how to find the intersection, union, complement and difference of two sets.
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Know the basics on sets such as the methods of writing sets, the cardinality of a set, null and universal sets, equal and equivalents sets, and many more.
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Reference:
Nivera, G. C. (2013), Grade 7 Mathematics: Pattern and Practicalities. Don Bosco Press Inc. Makati City, Philippines.
This will help you in illustrating operations on sets using Venn Diagram. Also, how to find the intersection, union, complement and difference of two sets.
For more instructional resources, CLICK me here!
https://tinyurl.com/y9muob6q
LIKE and FOLLOW me here!
https://tinyurl.com/ycjp8r7u
https://tinyurl.com/ybo27k2u
Know the basics on sets such as the methods of writing sets, the cardinality of a set, null and universal sets, equal and equivalents sets, and many more.
If you are looking for math video tutorials (with voice recording), you may download it on our YouTube Channel. Don't forget to SUBSCRIBE for you to get updated on our upcoming videos.
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Factor Theorem and Remainder Theorem. Mathematics10 Project under Mrs. Marissa De Ocampo. Prepared by Danielle Diva, Ronalie Mejos, Rafael Vallejos and Mark Lenon Dacir of 10- Einstein. CNSTHS.
Sum and Difference of Cubes. The sum or difference of two cubes can be factored into a product of a binomial times a trinomial. That is, x3 + y3 = (x + y)(x2 − xy + y2) and x3 − y3 = (x − y)(x2 + xy + y2) .
If you are looking for math video tutorials (with voice recording), you may download it on our YouTube Channel. Don't forget to SUBSCRIBE for you to get updated on our upcoming videos.
https://tinyurl.com/y9muob6q
Also, please do visit our page, LIKE and FOLLOW us on Facebook!
https://tinyurl.com/ycjp8r7u
https://tinyurl.com/ybo27k2u
Factor Theorem and Remainder Theorem. Mathematics10 Project under Mrs. Marissa De Ocampo. Prepared by Danielle Diva, Ronalie Mejos, Rafael Vallejos and Mark Lenon Dacir of 10- Einstein. CNSTHS.
Sum and Difference of Cubes. The sum or difference of two cubes can be factored into a product of a binomial times a trinomial. That is, x3 + y3 = (x + y)(x2 − xy + y2) and x3 − y3 = (x − y)(x2 + xy + y2) .
After going through this module, you are expected to:
• define well-defined sets and other terms associated to sets
• write a set in two different forms;
• determine the cardinality of a set;
• enumerate the different subsets of a set;
• distinguish finite from infinite sets; equal sets from equivalent sets
• determine the union, intersection of sets and the difference of two sets
Explore the foundational concepts of sets in discrete mathematicsDr Chetan Bawankar
Explore the foundational concepts of sets in discrete mathematics with this comprehensive PowerPoint presentation. Whether you are a student delving into the world of discrete structures or an enthusiast eager to understand the fundamentals, this presentation serves as an insightful guide.
This slide help in the study of those students who are enrolled in BSCS BSC computer MSCS. In this slide introduction about discrete structure are explained. As soon as I upload my next lecture on proposition logic.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
The Art Pastor's Guide to Sabbath | Steve ThomasonSteve Thomason
What is the purpose of the Sabbath Law in the Torah. It is interesting to compare how the context of the law shifts from Exodus to Deuteronomy. Who gets to rest, and why?
Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
How to Split Bills in the Odoo 17 POS ModuleCeline George
Bills have a main role in point of sale procedure. It will help to track sales, handling payments and giving receipts to customers. Bill splitting also has an important role in POS. For example, If some friends come together for dinner and if they want to divide the bill then it is possible by POS bill splitting. This slide will show how to split bills in odoo 17 POS.
We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as “distorted thinking”.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
3. LEARNING
OBJECTIVES
At the end of this session, you are expected to:
1. describe well defined sets, ,subsets, universal sets, null sets, and
cardinality of sets;
2. illustrate the union and intersection of sets and the difference of
two sets;
3. use Venn diagrams to represent sets, subsets, and set operations;
and
4. solve problems involving sets.
4. EXPLORATION
Go to page 2 of your book. Let’s consider the following list below.
Which does not belong to the group?
1. boat, kalesa, car, bus, airplane
2. carabao, chicken, cow, pig, goat
3. Bulacan, Pampanga, Batangas, Bataan, Tarlac
4. hexagon, quadrilateral, rectangle, rhombus, square
5. meter, centimeter, kilometer, square meter, decimeter
6. 2, 12, 24, 11, 30
5. EXPLORATION
If we removed one particular member which is not part of the group,
we can now describe the characteristics of the new formed group.
For instance.
boat, kalesa, car, bus, airplane
boat, car, bus, airplane
(kinds of transport that use fuel)
T = {kinds of transport that use fuel)
6. EXPLORATION
If we removed one particular member which is not part of the group,
we can now describe the characteristics of the new formed group.
For instance.
carabao, chicken, cow, pig, goat
carabao, cow, pig, goat
(animals with for legs)
A = {animals with four legs)
7. EXPLORATION
If we removed one particular member which is not part of the group,
we can now describe the characteristics of the new formed group.
For instance.
Bulacan, Pampanga, Batangas, Bataan, Tarlac
Bulacan, Pampanga, Bataan, Tarlac
(provinces in Central Luzon)
P = {provinces in Central Luzon)
8. EXPLORATION
If we removed one particular member which is not part of the group,
we can now describe the characteristics of the new formed group.
For instance.
hexagon, quadrilateral, rectangle, rhombus, square
quadrilateral, rectangle, rhombus, square
(shapes with four sides)
S = {shapes with four sides)
9. EXPLORATION
If we removed one particular member which is not part of the group,
we can now describe the characteristics of the new formed group.
For instance.
2, 12, 24, 11, 30
2, 12, 24, 30
(even numbers)
E = {even number)
11. ANSWER THE FOLLOWING
QUESTIONS:
1. How many groups are there?
2. Does each object belong to a group?
3. Is there an object that belongs to
more than one group? Which one?
12. DO YOU HAVE THESE GROUPS?
1. H = {kinds of hat)
2. P = {different polyhedrons}
3. T = {kinds of terrestrial tress}
4. N = {set of positive integers}
5. O = {objects in black and white color}
13. THE GROUPS THAT YOU HAVE JUST CREATED ARE
CALLED
SETS
may be thought of as a well-defined collection of objects.
the groups are called sets for as long as the objects in the
group share a characteristic and are thus, well defined.
the objects in the group are called elements (∈) or
members of the set.
14. WAYS OF DESCRIBING
SETS
1.Roster Notation or Listing Method
describing a set by listing each ∈ inside
the symbol { }.
Ex. T = {boat, car, bus, airplane}
15. WAYS OF DESCRIBING
SETS
2. Verbal Description Method
describing a set in words.
Ex. Set T is the set of transport that
uses fuel.
16. WAYS OF DESCRIBING
SETS
3. Set Builder Notation
lists the rules that determine whether an
object is an ∈ of the set rather than the actual
elements.
Ex.
T = {x | x is a kind of transport that uses fuel}
17. NOTICE THE
DIFFERENCE
1. T = {boat, car, bus, airplane}
2. Set T is the set of transport that uses
fuel.
3. T = {x | x is a kind of transport that
uses fuel}
18. LET’S
PRACTICE
A. Describe the set A = {red, orange,
yellow, green, blue, indigo, violet}
using:
1. Verbal description
2. Rule (Set builder notation)
19. LET’S
PRACTICE
Describe the set A = {red, orange,
yellow, green, blue, indigo, violet} using:
1. Verbal description
Set A is the set of the colors of the
rainbow
20. LET’S
PRACTICE
Describe the set A = {red, orange,
yellow, green, blue, indigo, violet} using:
2. Rule (Set builder notation)
A = {x|x is a color of the rainbow}
21. LET’S
PRACTICE
B. Write the elements of
E = {x|x is an integer less than 5 but
greater than - 2}
E = {4, 3, 2, 1, 0, -1}
22. LET’S EXPLORE FURTHER
In the given set below, how many
elements were listed?
E = {4, 3, 2, 1, 0, -1}
Ans: There are 6 elements listed
We can say that n(E) = 6
Cardinality of a set
23. LET’S EXPLORE
FURTHER
EQUAL SETS
Two sets that contain exactly
the same ∈.
Ex.
A = {r, a, i, l}
B = {l, i, a, r}
EQUIVALENT SETS
Two sets that contain equal
number of ∈.
Ex.
A = {1, 2, 3, 4}
B = { J, U, N, E}
Set A is
equivalent to
set B
(A ≈ B)
Set A is equal
to set B
(A = B)
24. LET’S
PRACTICE
A. Identify whether each set is ≈ or =.
A = {r, e, a, d}
B = {x|x is a letter in laptop}
Set C is the components of MAPEH
D = {d, e, a, r}
E = {1, 2, 3, 4, 5}
25. LET’S EXPLORE
FURTHER
UNIVERSAL SETS
A universal set (usually
denoted by U) is a set which
has elements of all the related
sets, without any repetition of
elements.
Ex. If A = {1,2,3} and B = {a,b,c},
then the universal set associated
with these two sets is given by
U = {1,2,3,a,b,c}
VENN DIAGRAM
U
A
1, 2, 3
B
a, b, c
26. LET’S EXPLORE
FURTHER
UNIVERSAL SETS
Try this:
If A = {2,3, 5, 9} and B = {1, 6, 7},
determine its universal set (U)
U = {1, 2, 3, 5, 6, 7, 9}
VENN DIAGRAM
U
A
2, 3, 5,
9
B
1, 6, 7
27. LET’S EXPLORE
FURTHER
SUBSET & PROPER
SUBSET
a set of which all the elements are
contained in another set.
Set A is a subset of B (A ⊆ B) if and
only if every element in A is also an
element in B.
Ex. If A = {1,5,7} and B = {1, 2, 3, 4, 5,
6, 7}, then A ⊆ B
If there is at least one element of set
B that is not an member of set A, we
call set A as the proper subset of B
(A ⊂ B)
VENN DIAGRAM
U
B
2, 3, 4,
6
A
1, 5, 7
30. LET’S
PRACTICE
List all the possible subsets of set given.
1. A = {m, a, t, h}
Zero at a
time
One at a
time
Two at a time Three at a
time
Four at a
time
31. LET’S
PRACTICE
List all the possible subsets of set given.
1. A = {m, a, t, h}
Which of the following subsets given are ⊂?
Zero at a
time
One at a
time
Two at a time Three at a
time
Four at a
time
{ } {m} {m, a} {m, a, t} {m, a, t, h}
{a} {m, t} {m, t, h}
{ t } {m, h} {a, t, h}
{h} {a, t)
{a, h}
{t, h}
32. OPERATIONS ON SETS
INTERSECTION OF SET
The intersection of sets A and
B (A ∩ B) is a set of elements
that are members of both A
and B.
Ex.
A = {1, 2, 4, 6, 8}
B = {2, 3, 4, 5, 6}
A ∩ B = {2, 4, 6}
VENN DIAGRAM
A ∩ B
33. OPERATIONS ON SETS
UNION OF SETS
The union of two sets (A ⋃ B)
contains all the elements
contained in either set (or
both sets).
Ex.
A = {1, 2, 4, 6, 8}
B = {2, 3, 4, 5, 6}
A ⋃ B = {1, 2, 3, 4, 5, 6, 8}
VENN DIAGRAM
Shaded region represents A ⋃ B
34. OPERATIONS ON SETS
DIFFERENCE OF TWO
SETS
The difference of two sets,
written A - B is the set of all
elements of A that are not
elements of B.
Ex.
A = {1, 2, 4, 6, 8}
B = {2, 3, 4, 5, 6}
A – B = {1, 8}
VENN DIAGRAM
Shaded region represents A – B
U
35. OPERATIONS ON SETS
COMPLIMENT OF A SET
The complement of a set (A’) is
the set that includes all the
elements of the universal set (U)
that are not present in the given
set.
Ex.
U = {1, 2, 3, 4, 5, 6, 7, 8, 9}
A = {1, 2, 4, 6, 8}
B = {2, 3, 4, 5, 6}
A’ = {3, 5, 7, 9}
VENN DIAGRAM
Shaded regions represents A’
U