This document contains a mathematics lesson plan for grade 7 on set operations and Venn diagrams. It includes an opening prayer, attendance, objectives for the lesson, explanations of sets and Venn diagrams, examples of how to identify elements in different areas of Venn diagrams based on set notations, and a drill for students to practice. The lesson teaches students to visualize relationships between sets using Venn diagrams and identify elements based on notations for union, intersection, complement, and difference of sets.
Sets is the first lesson in Mathematics 7. This lesson introduces the basic terms. For more presentations visit me on YouTube. https://www.youtube.com/channel/UCltDbhOXh6r9FyYE52rWzCQ/playlists?shelf_id=18&view_as=subscriber&sort=dd&view=50
Sets is the first lesson in Mathematics 7. This lesson introduces the basic terms. For more presentations visit me on YouTube. https://www.youtube.com/channel/UCltDbhOXh6r9FyYE52rWzCQ/playlists?shelf_id=18&view_as=subscriber&sort=dd&view=50
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
Learning Guide for Grade 7 Mathematics under the k-12 Curriculum in the Phili...polchan
This is the mathematics Module for Grade 7 pupils under the K-12 Curriculum implemented in the Philippines. This is a Learning Guide for Grade 7 Mathematics.
1 Sets It is natural for us to classify items into .docxShiraPrater50
1
Sets
It is natural for us to classify items into groups, or sets, and consider how those sets overlap
with each other. We can use these sets understand relationships between groups, and to
analyze survey data.
Basics
An art collector might own a collection of paintings, while a music lover might keep a
collection of CDs. Any collection of items can form a set.
Set
A set is a collection of distinct objects, called elements of the set.
A set can be defined by describing the contents, or by listing the elements of the set,
enclosed in curly brackets.
Example 1
Some examples of sets defined by describing the contents:
a) The set of all even numbers
b) The set of all books written about travel to Chile
Some examples of sets defined by listing the elements of the set:
a) {1, 3, 9, 12}
b) {red, orange, yellow, green, blue, indigo, purple}
A set simply specifies the contents; order is not important. The set represented by {1, 2, 3} is
equivalent to the set {3, 1, 2}.
Notation
Commonly, we will use a variable to represent a set, to make it easier to refer to that set
later.
The symbol ∊ means “is an element of”.
A set that contains no elements, { }, is called the empty set and is notated ∅
Example 2
Let A = {1, 2, 3, 4}
To notate that 2 is element of the set, we’d write 2 ∊ A
2
Sometimes a collection might not contain all the elements of a set. For example, Chris owns
three Madonna albums. While Chris’s collection is a set, we can also say it is a subset of the
larger set of all Madonna albums.
Subset
A subset of a set A is another set that contains only elements from the set A, but may
not contain all the elements of A.
If B is a subset of A, we write B ⊆ A
A proper subset is a subset that is not identical to the original set – it contains fewer
elements.
If B is a proper subset of A, we write B ⊂ A
Example 3
Consider these three sets
A = the set of all even numbers B = {2, 4, 6} C = {2, 3, 4, 6}
Here B ⊂ A since every element of B is also an even number, so is an element of A.
More formally, we could say B ⊂ A since if x ∊ B, then x ∊ A.
It is also true that B ⊂ C.
C is not a subset of A, since C contains an element, 3, that is not contained in A
Example 4
Suppose a set contains the plays “Much Ado About Nothing”, “MacBeth”, and “A
Midsummer’s Night Dream”. What is a larger set this might be a subset of?
There are many possible answers here. One would be the set of plays by Shakespeare. This
is also a subset of the set of all plays ever written. It is also a subset of all British literature.
Try it Now 1
The set A = {1, 3, 5}. What is a larger set this might be a subset of?
3
Union, Intersection, and Complement
Commonly sets interact. For example, you and a new roommate decide to have a house
party, and you both invite your circle of friends. At this party, two se ...
1 Sets It is natural for us to classify items into .docxpoulterbarbara
1
Sets
It is natural for us to classify items into groups, or sets, and consider how those sets overlap
with each other. We can use these sets understand relationships between groups, and to
analyze survey data.
Basics
An art collector might own a collection of paintings, while a music lover might keep a
collection of CDs. Any collection of items can form a set.
Set
A set is a collection of distinct objects, called elements of the set.
A set can be defined by describing the contents, or by listing the elements of the set,
enclosed in curly brackets.
Example 1
Some examples of sets defined by describing the contents:
a) The set of all even numbers
b) The set of all books written about travel to Chile
Some examples of sets defined by listing the elements of the set:
a) {1, 3, 9, 12}
b) {red, orange, yellow, green, blue, indigo, purple}
A set simply specifies the contents; order is not important. The set represented by {1, 2, 3} is
equivalent to the set {3, 1, 2}.
Notation
Commonly, we will use a variable to represent a set, to make it easier to refer to that set
later.
The symbol ∊ means “is an element of”.
A set that contains no elements, { }, is called the empty set and is notated ∅
Example 2
Let A = {1, 2, 3, 4}
To notate that 2 is element of the set, we’d write 2 ∊ A
2
Sometimes a collection might not contain all the elements of a set. For example, Chris owns
three Madonna albums. While Chris’s collection is a set, we can also say it is a subset of the
larger set of all Madonna albums.
Subset
A subset of a set A is another set that contains only elements from the set A, but may
not contain all the elements of A.
If B is a subset of A, we write B ⊆ A
A proper subset is a subset that is not identical to the original set – it contains fewer
elements.
If B is a proper subset of A, we write B ⊂ A
Example 3
Consider these three sets
A = the set of all even numbers B = {2, 4, 6} C = {2, 3, 4, 6}
Here B ⊂ A since every element of B is also an even number, so is an element of A.
More formally, we could say B ⊂ A since if x ∊ B, then x ∊ A.
It is also true that B ⊂ C.
C is not a subset of A, since C contains an element, 3, that is not contained in A
Example 4
Suppose a set contains the plays “Much Ado About Nothing”, “MacBeth”, and “A
Midsummer’s Night Dream”. What is a larger set this might be a subset of?
There are many possible answers here. One would be the set of plays by Shakespeare. This
is also a subset of the set of all plays ever written. It is also a subset of all British literature.
Try it Now 1
The set A = {1, 3, 5}. What is a larger set this might be a subset of?
3
Union, Intersection, and Complement
Commonly sets interact. For example, you and a new roommate decide to have a house
party, and you both invite your circle of friends. At this party, two se.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
Safalta Digital marketing institute in Noida, provide complete applications that encompass a huge range of virtual advertising and marketing additives, which includes search engine optimization, virtual communication advertising, pay-per-click on marketing, content material advertising, internet analytics, and greater. These university courses are designed for students who possess a comprehensive understanding of virtual marketing strategies and attributes.Safalta Digital Marketing Institute in Noida is a first choice for young individuals or students who are looking to start their careers in the field of digital advertising. The institute gives specialized courses designed and certification.
for beginners, providing thorough training in areas such as SEO, digital communication marketing, and PPC training in Noida. After finishing the program, students receive the certifications recognised by top different universitie, setting a strong foundation for a successful career in digital marketing.
More Related Content
Similar to Grade-7-C-Set Operatios and Venn Diagrams.pptx
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
Learning Guide for Grade 7 Mathematics under the k-12 Curriculum in the Phili...polchan
This is the mathematics Module for Grade 7 pupils under the K-12 Curriculum implemented in the Philippines. This is a Learning Guide for Grade 7 Mathematics.
1 Sets It is natural for us to classify items into .docxShiraPrater50
1
Sets
It is natural for us to classify items into groups, or sets, and consider how those sets overlap
with each other. We can use these sets understand relationships between groups, and to
analyze survey data.
Basics
An art collector might own a collection of paintings, while a music lover might keep a
collection of CDs. Any collection of items can form a set.
Set
A set is a collection of distinct objects, called elements of the set.
A set can be defined by describing the contents, or by listing the elements of the set,
enclosed in curly brackets.
Example 1
Some examples of sets defined by describing the contents:
a) The set of all even numbers
b) The set of all books written about travel to Chile
Some examples of sets defined by listing the elements of the set:
a) {1, 3, 9, 12}
b) {red, orange, yellow, green, blue, indigo, purple}
A set simply specifies the contents; order is not important. The set represented by {1, 2, 3} is
equivalent to the set {3, 1, 2}.
Notation
Commonly, we will use a variable to represent a set, to make it easier to refer to that set
later.
The symbol ∊ means “is an element of”.
A set that contains no elements, { }, is called the empty set and is notated ∅
Example 2
Let A = {1, 2, 3, 4}
To notate that 2 is element of the set, we’d write 2 ∊ A
2
Sometimes a collection might not contain all the elements of a set. For example, Chris owns
three Madonna albums. While Chris’s collection is a set, we can also say it is a subset of the
larger set of all Madonna albums.
Subset
A subset of a set A is another set that contains only elements from the set A, but may
not contain all the elements of A.
If B is a subset of A, we write B ⊆ A
A proper subset is a subset that is not identical to the original set – it contains fewer
elements.
If B is a proper subset of A, we write B ⊂ A
Example 3
Consider these three sets
A = the set of all even numbers B = {2, 4, 6} C = {2, 3, 4, 6}
Here B ⊂ A since every element of B is also an even number, so is an element of A.
More formally, we could say B ⊂ A since if x ∊ B, then x ∊ A.
It is also true that B ⊂ C.
C is not a subset of A, since C contains an element, 3, that is not contained in A
Example 4
Suppose a set contains the plays “Much Ado About Nothing”, “MacBeth”, and “A
Midsummer’s Night Dream”. What is a larger set this might be a subset of?
There are many possible answers here. One would be the set of plays by Shakespeare. This
is also a subset of the set of all plays ever written. It is also a subset of all British literature.
Try it Now 1
The set A = {1, 3, 5}. What is a larger set this might be a subset of?
3
Union, Intersection, and Complement
Commonly sets interact. For example, you and a new roommate decide to have a house
party, and you both invite your circle of friends. At this party, two se ...
1 Sets It is natural for us to classify items into .docxpoulterbarbara
1
Sets
It is natural for us to classify items into groups, or sets, and consider how those sets overlap
with each other. We can use these sets understand relationships between groups, and to
analyze survey data.
Basics
An art collector might own a collection of paintings, while a music lover might keep a
collection of CDs. Any collection of items can form a set.
Set
A set is a collection of distinct objects, called elements of the set.
A set can be defined by describing the contents, or by listing the elements of the set,
enclosed in curly brackets.
Example 1
Some examples of sets defined by describing the contents:
a) The set of all even numbers
b) The set of all books written about travel to Chile
Some examples of sets defined by listing the elements of the set:
a) {1, 3, 9, 12}
b) {red, orange, yellow, green, blue, indigo, purple}
A set simply specifies the contents; order is not important. The set represented by {1, 2, 3} is
equivalent to the set {3, 1, 2}.
Notation
Commonly, we will use a variable to represent a set, to make it easier to refer to that set
later.
The symbol ∊ means “is an element of”.
A set that contains no elements, { }, is called the empty set and is notated ∅
Example 2
Let A = {1, 2, 3, 4}
To notate that 2 is element of the set, we’d write 2 ∊ A
2
Sometimes a collection might not contain all the elements of a set. For example, Chris owns
three Madonna albums. While Chris’s collection is a set, we can also say it is a subset of the
larger set of all Madonna albums.
Subset
A subset of a set A is another set that contains only elements from the set A, but may
not contain all the elements of A.
If B is a subset of A, we write B ⊆ A
A proper subset is a subset that is not identical to the original set – it contains fewer
elements.
If B is a proper subset of A, we write B ⊂ A
Example 3
Consider these three sets
A = the set of all even numbers B = {2, 4, 6} C = {2, 3, 4, 6}
Here B ⊂ A since every element of B is also an even number, so is an element of A.
More formally, we could say B ⊂ A since if x ∊ B, then x ∊ A.
It is also true that B ⊂ C.
C is not a subset of A, since C contains an element, 3, that is not contained in A
Example 4
Suppose a set contains the plays “Much Ado About Nothing”, “MacBeth”, and “A
Midsummer’s Night Dream”. What is a larger set this might be a subset of?
There are many possible answers here. One would be the set of plays by Shakespeare. This
is also a subset of the set of all plays ever written. It is also a subset of all British literature.
Try it Now 1
The set A = {1, 3, 5}. What is a larger set this might be a subset of?
3
Union, Intersection, and Complement
Commonly sets interact. For example, you and a new roommate decide to have a house
party, and you both invite your circle of friends. At this party, two se.
Similar to Grade-7-C-Set Operatios and Venn Diagrams.pptx (20)
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Safalta Digital marketing institute in Noida, provide complete applications that encompass a huge range of virtual advertising and marketing additives, which includes search engine optimization, virtual communication advertising, pay-per-click on marketing, content material advertising, internet analytics, and greater. These university courses are designed for students who possess a comprehensive understanding of virtual marketing strategies and attributes.Safalta Digital Marketing Institute in Noida is a first choice for young individuals or students who are looking to start their careers in the field of digital advertising. The institute gives specialized courses designed and certification.
for beginners, providing thorough training in areas such as SEO, digital communication marketing, and PPC training in Noida. After finishing the program, students receive the certifications recognised by top different universitie, setting a strong foundation for a successful career in digital marketing.
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2. Dear Lord and Father of all,
✗ Thank you for today.
✗ Thank you for ways in which you provide for us all.
✗ For Your protection and love we thank you. Help us
to focus our hearts and minds now on what we are
about to learn.
✗ Inspire us by Your Holy Spirit as we listen and write.
✗ Guide us by your eternal light as we discover more
about the world around us.
✗ We ask all this in the name of Jesus.
✗ Amen.
2
3. 1.Be on time.
2.Always turn on your
camera.
3.Unmute your audio
when called by your
teacher.
3
4.Do have your module,
notebook and pen.
5.Questions will be
entertained after a
discussed topic.
6.Be attentive and enjoy
learning.
6. Looking Back at your Lesson
✗ From the previous module, you have learned that a set is a well-
defined group of objects, called elements, which share a common
characteristic. The different set operations are:
✗ 1. Union of Sets: The union of the sets A and B,
denoted by A∪B, is the set that contains those
elements that belong to A, B, or to both.
✗ 2. Intersection of Sets: The intersection of the sets A
and B, denoted by A∩B, is the set containing those
elements that belong to both A and B.
6
7. Looking Back at your Lesson
✗ From the previous module, you have learned that a set is a well-
defined group of objects, called elements, which share a common
characteristic. The different set operations are:
✗ 3. Complement of a Set: The complement of a set A,
written as A’, is the set of all elements found in the
universal set, U, that are not found in set A.
✗ 4. Difference of Sets: The difference of two sets,
written as A – B, is the set of all elements of A that are
not elements of B.
7
8. Looking Back at your Lesson
✗ Given: U = { a, b, c, d, e, f, g, h, i, j } , M = { a, b, c, d, e },
N = { i, g, h}, A = { a, c, e, h, i, j }
✗ Which elements match each set?
✗ 1. A ∪ M
✗ 2. A ∩ M
✗ 3. M’
✗ 4. M – N
✗ 5. N – M
8
10. Venn Diagram Defined
A Venn Diagram refers to the diagram that shows the relationship
between and among sets of objects. It was first introduced by the
mathematician John Venn in 1880s.
This diagram enables you to organize information visually so that
you can see the relationships between two or three sets of items.
You can then identify similarities and differences. You can also
determine what elements are in a set and what elements do not
belong to the set.
A Venn diagram consists of two or more overlapping closed
curves, usually circles, each representing a set.
10
11. Visualizing the different regions in a Venn diagram
The idea of the Venn Diagram is simple: sets are
shown as regions.
The inside of the circle represents elements of a
set, the outside contains anything that is not in
that set. Shown on the right is an example of a
Venn Diagram. By convention, capital letters are
used to denote sets. If you happen to see small
letters, consider these small letters as elements.
Braces,{ }, denote a list of elements in a set.
11
12. Venn Diagram
Set Notation
1. Set A
Venn Diagram
Explanation
This set includes the elements common to
both A and B and the elements only in A.
12
13. Venn Diagram
Set Notation
2. Set B
Venn Diagram
Explanation
This set includes the elements common to
both A and B and the elements only in B.
13
14. Venn Diagram
Set Notation
3. A∩B
Venn Diagram
Explanation
This set contains elements that are common
to both A and B.
14
15. Venn Diagram
Set Notation
4. A – B
Venn Diagram
Explanation
This set contains elements of A that are not
elements of B.
15
16. Venn Diagram
Set Notation
5. B – A
Venn Diagram
Explanation
This set contains elements of B that are not
elements of A.
16
17. Venn Diagram
Set Notation
6. A∪B
Venn Diagram
Explanation
This set contains elements that belong to A,
B, or to both.
17
18. Venn Diagram
Set Notation
7. A’
Venn Diagram
Explanation
This set contains elements of the Universal
Set that are not in Set A.
18
19. EXAMPLE # 1: Given the Venn diagram below,
find the elements of the following:
1. Set P
Answer: P = {3, 6, 9}. The
elements that you can find in
P are 3, 6, and 9.
2. Set Q
Answer: Q = {2, 4, 6, 8}. The
elements that you can find in
Q are 2, 4, 6, and 8.
19
20. Given the Venn diagram below, find the elements
of the following:
3. P∩Q
Answer: P∩Q = {6}. This is
because 6 is the element
common to both P and Q.
4. P – Q
Answer: P – Q = {3, 9}. This is
because 3 and 9 are the
elements of P that are not in Q.
20
21. Given the Venn diagram below, find the elements
of the following:
5. Q – P
Answer: Q – P = {2, 4, 8}. This
is because 2, 4, and 8 are
elements of Q that are not in P.
6. P∪Q
Answer: P∪Q = {2, 3, 4, 6, 8, 9}.
This set contains elements in P,
Q, or both P and Q.
21
22. Given the Venn diagram below, find the elements
of the following:
7. P’
Answer: P’ = {0, 1, 2, 4, 5, 7, 8}.
This set contains elements of
the universal set which are not
in P.
22
23. DRILL: Given the Venn diagram below, find the
elements of the following:
1. Set A
Answer: A = {1, 3, 5, 7, 9, 11}
2. Set B
Answer: B = {2, 3, 5, 7, 11}
3. A∩B
Answer: A∩B = {3, 5, 7, 11}
23
24. DRILL: Given the Venn diagram below, find the
elements of the following:
4. A – B
Answer: A – B = {1, 9}
5. B – A
Answer: B – A = {2}
6. A∪B
Answer: A∪B = {1, 2, 3, 5, 7, 9,
11}
24
25. DRILL: Given the Venn diagram below, find the
elements of the following:
7. A’
Answer: A’ = {2, 4, 6, 8, 10}
25