MAT
Name: ___________________________
Gr.& Section: _____________________
HEM Learning Module 1
FIRST QUARTER
ATIC
“Sets and Venn Diagram”
1) Sets
S7
The following topics are included in this module:
2) Relation on Set
3) Operations on Set
4) Problem-Solving Involving Set
In this module, you are expected to meet the following competencies:
1) Illustrate well-defined sets, subsets, universal sets, and the null set and cardinality of sets;
2) Illustrate the union and intersection of sets and the difference of two sets;
3) Use and draw Venn Diagrams to represent sets, subsets, and set operations;
4) Classify similarities and differences within the objects around them;
5) Solve problems involving sets; and
6) Practice systematic way of organizing things and real-life problems.
Pre–
Refer to the Answer Key found on the last page of this module to check your answers.
Day 1: Sets (Synchronous Session)
CONCEPT NOTES
Set – is a well-defined collection of objects.
Element – is a distinct object of the set.
Well-defined set – is the possibility to tell what objects belong to the set and what objects do not belong to
the set.
Cardinal number – is the number of elements in a set.
THREE WAYS IN DESCRIBING A SET
1. Rule Method – is a well-defined description of the elements of the given set.
2. Tabulation or Roster Method – is explicit listing or enumeration of the elements.
3. Set-builder Notation – uses a rule, formula, or a condition which must be possessed by all of the
elements in the set.
S={x│x has the common characteristics}
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*This read as “Set S is the set of all x such that x”, the vertical bar (|) replaces the words “such that”.
ILLUSTRATION
1. S = {Science, Filipino, English}
Science, Filipino and English are the elements of set S. The cardinal number of the set is three.
2. Z = {Science, Filipino, English}
Science, Filipino and English are the elements of set Z. The cardinal number of the set is three.
*Note: If no given name of set, use any letter in the English Alphabet. If a set contains many elements, we
use three dots (…) called ellipsis.
Roster Method Rule Method Set Builder
V = {a, e, i, o, u} V is the set of vowels in the V = {x|x is a vowel in the
English alphabet. English alphabet}
D = {Tuesday, Thursday} D is the set of days that D = {x|x is a day that begins with
begin with T. letter T}
EXERCISE NO. 1.1
Directions: Complete the table. Write the appropriate ways of writing sets and its cardinality.
Roster Method Rule Method Set Builder Cardinality
C is the set of all
continents.
G= {x|x is a planet in the solar
system}
Day 2: Relation on Sets (Synchronous Session)
CONCEPT NOTES
Sets are actually classified according to the elements they contain.
1. Empty set – is a set that contains no element. It is also called “null set” denoted by { ∅ } .
2. Unit set – is a set that has only one element. The cardinal number of a unit set is always 1.
3. Finite set – is a set that contains a countable number of elements and with a first and last element.
4. Infinite set – is a set that does not contain a countable number of elements.
5. Disjoint sets – are two sets that have no element in common.
6. Equal sets – are determined if and only if the two sets have exactly the same elements.
7. Equivalent sets – are two sets which have the same number of elements or the same cardinality. The
elements in this kind of set may not be the same.
ILLUSTRATION
1. B = {the set of odd numbers divisible by 2} is an example of null set since only even numbers are
divisible by 2.
2. A = {the set of positive square integer between 2 and 5} is a unit set since the only element that satisfies
the given condition in set A is 4.
3. D = {2, 3, 5, 7,12, 23} is an example of a finite set since there is a countable member of the given set D.
4. E = {the set of counting numbers} is an example of an infinite set since there is an infinite number of
elements in the set E.
5. B = {a, e, i, o, u} and B = {b, c, d, g, h, y, z} are examples of disjoint sets since these are two sets which
have no common element.
6. R = {x│x is an odd number between 4 and 8} R = {5, 7}
S = {y│y is a prime number between 4 and 10} R = {5, 7}
*The given sets are examples of equal sets since the two sets contain exactly the same elements.
7. A = {Luzon, Visayas, Mindanao} and D = {red, white, blue} are examples of equivalent sets because the
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two sets have the same cardinality.
EXERCISE NO. 1.2
Write your answers on a Learning Activity Sheet.
Directions: Create a Roster method set based on the given rules below. Then, identify the kind/s of set for each
given, Do not forget to use ellipsis if needed.
1. H is a set of even numbers from one to twenty.
2. O is a set of days the sun will be seen at 9PM in Cavite.
3. P and E are sets in which P is a set of even numbers from one to ten while E is a set of odd numbers from one to
ten.
4. A is a set of counting numbers.
Day 3: (Asynchronous Session)
Review the lessons in Day 1 and 2 and answer the activities given below. Also, do an advance reading
of Day 4 lesson.
Activity no. 1.1
Time started: ______
Time finished: ______
Write your answers on a Learning Activity Sheet.
A. Directions: Identify the method used in writing the sets below.
1. D = {x|x is a color in the rainbow}
2. R is a set of the months in a year.
3. E = {10, 20, 30, 40, 50, …}
4. A is a set of teachers you have in your class.
5. M = {x|x is a number divisible by 2}
B. Directions: Classify the following sets.
1. H = {The set of persons living in a house}
2. E = {The set of numbers which are multiples of 3}
3. R = {The set of whole numbers lying between 0 and 2}
4. F = {The set of triangles having 4 sides}
5. A = {3, 5, 9, 13} B = {2, 3, 4, 5}
Day 4: Operation of Sets (Synchronous Session)
CONCEPT NOTES
Venn diagram – It is a pictorial representation involving relations between and among sets. It consists
closed curves such as circles, drawn to show the elements of different sets and their combinations.
OPERATIONS OF SET
Union – is the set of all elements found in A or B. The union of sets A and B is denoted by A B (read as
“A union B”)
Intersection – is the set of all elements common to both A and B. It is denoted by A B (read as “A
intersection of B”)
Difference – is denoted as A – B is a new set which those elements belong to A but not in B.
Other types of sets such as:
Universal Set – is the set of all elements being considered. It is denoted by U.
Complement of a Set – is the set of all elements in the universal set that are not found in a given set and is
denoted by A’ (read as “A prime”).
ILLUSTRATION
Given the universal set U = {5, 6, 7, 8, 9,10,11,12}, list the elements of the set:
F = {x│x is a factor of 60} b. P = {y│y is a prime number}
Solution:
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The elements of Sets F and P can only be selected from the universal Set U.
F = {5, 6, 10, 12} P = {5, 7,11}
We can draw the Venn diagram to pictorially represent the universal set given above.
U Therefore, the elements, 8 and 9 were placed
outside the circles because they don’t belong to
either of the sets F and P. Still they are part of the
universal set U.
Then, the F ∪ P = {5, 6, 7, 10, 11, 12} and the F∩ P = {5}.
Just a little fact, the word “or” suggests union. In fact, “or” is to union as “and” is to intersection.
For more detailed explanation, refer to your book “Grade 7 Mathematics Patterns and
Practicalities” pages 22-25
EXERCISE NO. 1.3
Write your answers on a Learning Activity Sheet.
A. Directions: Draw a Venn diagram to represent the following sets in the problem. Write your answer on
a separate sheet of paper.
1. A bakery offers the pastries in the universal set; U = {donut, cupcake, cake, biscuit, muffin, brownie,
tart}. Raina (A) ordered donut, cake and muffin while Laidel (B) bought cake, brownie, and tart. Find the
intersection and union of set A and B, and complement of B.
B. Directions: Answer Comprehension Check number 11 letters a, b, e, and f on page 30 of your book.
Day 5: Problem-Solving Involving Sets (Synchronous Session)
CONCEPT NOTES
Venn diagram is used to solve simple logical problems. The universal set is represented by a
rectangle and all other sets under consideration by circles within the rectangle.
The following should be remembered in answering word problems involving sets:
a. Read the question carefully and list down all key information.
b. Know the standard parts of a Venn diagram.
c. Work in a step-by-step manner.
d. Check at the end that all the numbers add up correctly.
ILLUSTRATION
Let A and B be two finite sets such that n(A) = 20, n(B) = 28 and n(AUB)=36. Find n(A∩B).
Step 1. Determine what is given and what are being asked.
Given : Asked:
n (A) = 20 Find n (A∩ B)
n (B) = 28
n (A U B) = 36
Step 2. Illustrate using the Venn diagram if possible. The Venn diagram is shown below:
Step 3. Determine what operations to be used.
Using the formula n (A U B) = n (A) + n (B) – n (A ∩ B), then:
n (A ∩ B) = n (A) + n (B) – n (A U B)
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n (A ∩ B) = 20 + 28 – 36
n (A ∩ B) = 48 – 36
n (A ∩ B) = 12
Step 4. Substitute the values in the Venn diagram
EXERCISE NO. 1.4
Write your answers on a Learning Activity Sheet.
Directions: Make a Venn diagram for the word problem below. Answer the questions afterwards.
A survey asked 20 students whether they will join the music club or journalism club. Three students will
join music and journalism club, 8 will join music club and 5 in journalism.
a. How many students will not join any club?
b. How many students will join music club only?
c. How many students will join journalism club only?
d. How many students will join both clubs and music club?
Post –
Let us test what you have learned after accomplishing this module. Read the directions carefully and
answer the test below.
KNOWLEDGE
Directions: Change the following Roster method into set builder notation.
1. A= {1,3,5,7,9}
2. B= {January, March, May, July, August, October, December}
3. C= {3,6,9,12,15, …}
PROCESS
Directions: Create your own word problem involving sets and draw a Venn diagram to represent the given
data in your word problem.
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CRITERIA 4 points 3 points 2 points 1 point
Gives the right and Gives the right
complete solution, the Gives the right solution, the Gives the right solution solution but the
Solving answer is correct and answer is correct and shows correct answer but there answer is incorrect
shows very neat work neatness of work. are erasures. and there are
presentation. erasures
Processing Question (1 point):
1. Which topics did you consider as you answered the given problems on each item? How did these topics
help you?
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UNDERSTANDING
Directions: Read the given question carefully. Then, write a reflection in not less than five (5) sentences.
Please be guided by the provided criteria below.
Criteria 4 3 2 1
Uses inconsistent
Uses clear
Uses clear, consistent Uses consistent organizational
organizational strategy
Organization organizational organizational strategy; strategy;
with occasional
strategy. presentation is logical. presentation is not
inconsistencies.
logical.
The answer is The answer is focused The answer poorly
The answer is focused
focused, purposeful, on topic and includes addresses topic and
Content on the topic and
and reflects original few loosely related includes irrelevant
includes relevant ideas.
insight and ideas. ideas. ideas.
1. If you are to create a set base on your likes and dislikes, how will it look like? What kind of set is it?
Present your answer using the first and second letters of your name.
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Reference
1) Gladys C. Nievera Phd. Grade 7 Mathematics Patterns and Practicalities
Answer
Key
Here are the answers in pre-test. Please look at this part, only after accomplishing the pre-test.
HONESTY IS STILL THE BEST POLICY. Please check your answers and determine how much
knowledge you have attained.
Pre-Test
Let set
A = set of animals Set A = {giraffe, lion, rabbit}
B = set of fruits Set B = {banana, pineapple, watermelon}
C = set of vegetables Set C = {carrots, cabbage, squash}
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