Mathematics 7 Quarter 1 Module 1: Sets

Mathematics Quarter 1 – Module 1: Sets

7

Mathematics

Quarter 1 – Module 1:

Sets

CO_Q1_MATHEMATICS 7_Module 1

[illustration: students and a teacher at school, with a globe, a lantern, and a child writing]

Mathematics – Grade 7 Alternative Delivery Mode Quarter 1 – Module 1: Sets First Edition, 2020

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Published by the Department of Education Secretary: Leonor Magtolis Briones Undersecretary: Diosdado M. San Antonio

Development Team of the Module
Writers:	Michelle Ann C. Caras, Melanie G. Sasota, Rose Grace A. Galan
Editors:	Randy L. Pendilla, Raul L. Pojas, Shienna Lyn L. Antenor and Iza Agrazamendez
Reviewers:	Evelyn C. Frusa, PhD, Noemi E. Parcon, Rolex H. Lotilla and Arvin Tejada
Illustrator:	Michelle Ann C. Caras
Layout Artist:	Arianne N. Tagolino
Management Team:	Dr. Allan G. Farnazo, CESO IV – Regional Director Gilbert B. Barrera – Chief, CLMD Arturo D. Tingson Jr. – REPS, LRMS Peter Van C. Ang-ug – Regional ADM Coordinator Belen L. Fajemolin, PhD – CID Chief Evelyn C. Frusa, PhD – Division EPS In Charge of LRMS

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Introductory Message

This Self-Learning Module (SLM) is prepared so that you, our dear learners, can continue your studies and learn while at home. Activities, questions, directions, exercises, and discussions are carefully stated for you to understand each lesson.

Each SLM is composed of different parts. Each part shall guide you step-by- step as you discover and understand the lesson prepared for you.

Pre-test are provided to measure your prior knowledge on lessons in each SLM. This will tell you if you need to proceed on completing this module, or if you need to ask your facilitator or your teacher’s assistance for better understanding of the lesson. At the end of each module, you need to answer the post-test to self-check your learning. Answer keys are provided for each activity and test. We trust that you will be honest in using these.

In addition to the material in the main text, Notes to the Teachers are also provided to the facilitators and parents for strategies and reminders on how they can best help you on your home-based learning.

Please use this module with care. Do not put unnecessary marks on any part of this SLM. Use a separate sheet of paper in answering the exercises and tests. Read the instructions carefully before performing each task.

If you have any questions in using this SLM or any difficulty in answering the tasks in this module, do not hesitate to consult your teacher or facilitator.

Thank you.

What I Need to Know

This module was designed and written with you in mind. It is here to help you master the Sets. The scope of this module permits it to be used in many different learning situations. The language used recognizes the diverse vocabulary level of students. The lessons are arranged to follow the standard sequence of the course. But the order in which you read them can be changed to correspond with the textbook you are now using.

The module contains lessons on:

• Lesson 1 – Sets
• Lesson 2 – Subset, Universal Sets, Null Set, Cardinality of Sets
• Lesson 3 – Union and Intersection of Sets and the Difference of Two Sets

After going through this module, you are expected to:

1. define a well-defined set;
2. illustrate a subset, universal set, null set, cardinality of set; and
3. analyze union, intersection, and the difference of two sets.

What I Know

Select the correct answer. Write the letter on a separate sheet of paper.

1. Which of the following is a well-defined set?
   a. A set of beautiful sceneries
   b. A set of good basketball players
   c. A set of Philippine Presidents
   d. A set of successful leaders.

   
   

2. List all the letters in the word “school”.
   a. {s, c, h, o, o, l} c. {s, h, o, o, l}
   b. {s, c, h, o, l} d. {s, c, o, l}

   
   

3. Which of the following is the symbol of an empty set?
   a. ∩ b. ∪ c. ⊆ d. ∅

   
   

4. Which of the following is a subset of A= {1,2,3}?
   a. {0} b. {0,1} c. {1,2} d. {2,3,4}

   
   

5. Given the set of letters in the word “mathematics”, what is the cardinality of the given set?
   a. 11 b. 8 c. 6 d. 4

   
   

[illustration: hand pressing a finger, icon beside “What I Need to Know”]

[illustration: hand holding a pencil, icon beside “What I Know”]

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6. Which symbol is used to indicate the intersection of two sets?
   a. ∪ b. ∩ c. – d. ∅

   
   

7. Which symbol is used to indicate the union of two sets?
   a. ∅ b. ∪ c. ∩ d. –

   
   

*For numbers 8 – 10, use the following: A = {1, 2, 4, 5, 6} B = {1, 3, 5, 7}, C = {2, 4, 6, 8}

8. Find A ∪ B
   a. {1, 2, 3, 4, 5, 6, 7} c. {3}
   b. {1, 2, 3, 4, 5, 7, 8} d. {1, 3, 4, 5, 7, 8}

   
   

9. Find B ∩ C
   a. {0, 2, 3} c. { }
   b. {0, 2, 3, 5, 6, 7, 8} d. {8}

   
   

10. Find A – B
    a. {1,2,4} c. {3}
    b. {5,7,8} d. {2, 4, 6}

    
    

11. The following is a subset of R = {n, e, w}, EXCEPT?
    a. {n, e, w} b. {e} c. {0} d. { }

    
    

12. Which of the following set has the cardinality equals to 5?
    a. Set A is the set of counting numbers less than 5.
    b. Set B is the set of letters in the word “RACER”.
    c. Set C is the set of positive multiples of 5.
    d. Set D is the set of names of the fingers.

    
    

13. Given A = {i, c, e} and B = {c, o, l, d}, find A∪B.
    a. {c, o, l, d, i, e} b. {i, e} c. {e} d. { }

    
    

14. Given A = {5, 10, 15, 20} and B = {25}, find A ∩ B.
    a. {5, 10, 15, 20, 25} b. {5, 10, 15, 20} c. { } d. {0}

    
    

15. Given E = {pig, goat, cow, horse} and F = {chicken, duck}, find E – F.
    a. {pig, goat, cow, horse, chicken, duck}
    b. {pig, goat, cow, horse}
    c. {chicken, duck}
    d. { }

    
    

3

In this lesson you will learn how to define and illustrate a well-defined set and to identify the elements of the given set.

[illustration: hand holding a puzzle piece, icon beside “What’s In”]

Lesson 1 Sets

What’s In

Group and label the objects below according to their characteristics. Write your answer on a separate sheet of paper.

[illustration: nine numbered objects: 1 a flower, 2 an apple, 3 a butterfly, 4 a pear, 5 a tulip bud, 6 a butterfly, 7 a flower, 8 an egg, 9 a butterfly]

After you label and group the objects, answer the following questions:

a. Why did you group the object as such? b. How many groups are there? c. What are the names of the groups created?

Notes to the Teacher

This activity will guide you to let the students describe and illustrate the set.

4

What’s New

In the collections of objects below, which does not belong to the group?

[illustration: four plane shapes: a triangle, a long obtuse triangle, a right triangle, and a trapezoid]

What is It

Sets

The groups are called sets. Set maybe thought as a collection of objects.

Example:

[photo: a set of mountains] [illustration: a set of books] [illustration: a set of buildings]

WELL – DEFINED SET

In mathematics, set is a well-defined group or collection of objects that share common characteristics. The objects contained in the set are called elements.

A set can be named using capital letters like A, B, C, D,…Z and we use braces { } to group the elements of set separated by commas.

If a set contains many elements, we often use three dots, …, called ellipsis.

*Note: In listing the elements of the set, each distinct element is listed once and the order of the element does not matter.

Example of well-defined sets

1. The set of primary colors
   M = {red, yellow, blue}
2. The set of all even numbers.
   E = { 2, 4, 6,…}
3. The set of all multiples of 5.
   Y = {5, 10, 15, …}
4. The set of letter in the word “arrange”.
   O = { a, r, n, g, e}

Example of not well-defined sets

1. The set of famous dancers.
2. The set of punctual students in your class.
3. The set of honest people

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*Note: The sets given above are not well-defined since people will have different point of views on famous dancers, punctual students and honest people.

What’s More

State whether each of the following sets is well-defined or not. Write your answer in the space provided before the number.

_____ 1. The set of young politicians. _____ 2. The set of types of matter. _____ 3. The set of versatile actress. _____ 4. The set of all oceans of the earth. _____ 5. The set of months containing 31 days. _____ 6. The set of tasty food. _____ 7. The set of planets in our solar system. _____ 8. The set of durable bags. _____ 9. The set of consonants in the English Alphabet _____ 10. The set of even counting numbers.

What I Have Learned

Match the descriptions in column A with word/s being described in column B. Write the letter of your answer in the space provided

Column A	Column B
_____ 1. The objects contained in the set.	a. capital letters
_____ 2. A well-defined group or collection of objects that share common characteristics.	b. set
_____ 3. It is represented by three dots which is use to indicate that a set has many / infinite elements.	c. ellipsis
_____ 4. A symbol use to group the elements of a set.	d. { }
_____ 5. A symbol used to represent a set.	e. elements

What I Can Do

1. Which of the following is the set of animals living in water?
   a. A = {dolphin, whale, milk fish} c. C = {duck, chicken, turkey}
   b. B = {lion, buffalo, deer} d. D = {eagle, parrot, dove}

   
   

2. Given: A = {b, i, o, d, e, g, r, a, d, a, b, l, e}, which of the following is INCORRECT?
   a. It uses capital letter to name set. c. It uses braces.
   b. It does not list the object once. d. It uses commas.

   
   

3. The set of provinces in Region 12.
   a. E = {Aklan, Antique, Capiz, Guimaras, Ilo-ilo, Negros Occidental}
   b. F = {South Cotabato, North Cotabato, Sultan Kudarat, Sarangani, General Santos}
   c. G = {Ilocos Norte, Ilocos Sur, La Union, Pangasinan}
   d. H = {Cavite, Laguna, Batangas, Rizal, Quezon}

   
   

4. The set of months containing 30 days.
   a. I = {January, March, May} c. K = {June, July, August}
   b. J = {February, April, June} d. L = {June, September, November}

   
   

5. The set of secondary colors.
   a. M = {red, green, yellow} c. O = {green, orange, violet}
   b. N = {brown, pink, blue} d. P = {white, black, grey}

   
   

6. The set of vowels.
   a. Q = {a, e, i, o, u} c. S = {h, i, j, k, l}
   b. R = {c, d, e, f, g} d. T = {o, s, t, u, v}

   
   

7. Which of the following set is multiples of 2 and less than 12?
   a. U = {2, 10} c. W = {2, 4, 6, 8}
   b. V = {2, 4, 6} d. X = {2, 4, 6, 8, 10}

   
   

8. Which of the following is the set of odd whole numbers between 0 and 10?
   a. Y = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} c. A = {1, 3, 5, 7, 9}
   b. Z = {0, 2, 4, 6, 8, 9} d. B = {1, 3, 5, 7}

   
   

9. Name the next 3 elements of V = {3, 5, 7, 9, 11, … }.
   a. {12, 13, 14} c. {13, 14, 15}
   b. {12, 14, 16} d. {13, 15, 17}

   
   

10. Name the next 5 elements of E = {2, 4, 6, … }.
    a. {7, 8, 9, 10, 11} c. {8, 9, 10, 11, 12}
    b. {7, 9, 11, 13, 15} d. {8, 10, 12, 14, 16}

    
    

Lesson 2: Subsets, Universal Sets, Null Sets and Cardinality of Sets

In Lesson 1, you have learned how to illustrate sets. Now, you will learn about Subsets, Universal Sets, Null Sets and Cardinality of Sets.

What’s In

MEMORY CHECK!

Identify whether each of the following sets is well-defined or NOT. Put a check mark (/) if it is well-defined and a cross mark (x) if it is not. Write your answer in the space provided before the number.

_____ 1. The set of all even numbers from 2 to 10. _____ 2. The set of all factors of 18. _____ 3. The set of responsible citizens. _____ 4. The set of letters in the word “FATHER”. _____ 5. The set of hardworking front liners.

Notes to the Teacher

This activity will help the students recall the basic concepts of sets.

What’s New

Given: A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Find:

1. The set of odd numbers. 2. The set of all factors of 10.
2. The set of multiples of 4. 4. The set of negative integers.

What is It

UNIVERSAL SET

The universal set U is the set that contains all objects under consideration.

Examples:

1. Set U contains the set of whole numbers.
   U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, …}

   
   

2. Set U contains the set of all letters of the English Alphabet.
   U = {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z}

   
   

3. Set U contains the set of days of the week.
   U = {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}

   
   

SUBSETS

Given any two sets A and B, if every element in A is also an element in B, then A is a subset of B. The symbol “A ⊆ B” is read A is a subset of B.

*Note: Every set is a subset of itself and empty set is also a subset of every set.

Example:

1. R = {1, 2}

The possible subsets are;

Two Elements	One Element	Zero Element
{1,2}	{1}	{ } or ∅
	{2}

2. O = {red, blue, yellow}

The possible subsets of O are;

Three Elements	Two Elements	One Element	Zero Element
{red, blue, yellow }	{red, blue }	{ red }	{ } or ∅
	{red, yellow }	{ blue }
	{ blue, yellow }	{ yellow }

3. S = {3, 6, 9, 12}

The possible subsets of set S are;

Four Elements	Three Elements	Two Elements	One Element	Zero Element
{3, 6, 9, 12}	{3, 6, 9}	{3, 6}	{3}	{ } or ∅
	{3, 6, 12}	{3, 9}	{6}
	{3, 9, 12}	{3, 12}	{9}
	{6, 9, 12}	{6, 9}	{12}
		{6, 12}
		{9, 12}

4. E = {m, a, t, h}

[transcriber’s note: the table heading for item 4 reads “The possible subsets of set S are;” although the set is E]

The possible subsets of set S are;

Four Elements	Three Elements	Two Elements	One Element	Zero Element
{m, a, t, h}	{m, a, t}	{m, a}	{m}	{ } or ∅
	{m, a, h}	{m, t}	{a}
	{m, t, h}	{m, h}	{t}
	{a, t, h}	{a, t}	{h}
		{a, h}
		{t, h}

5. G = {0, 2, 4, 6, 8}

The possible subsets of set G are;

Five Elements	Four Elements	Three Elements	Two Elements	One Element	Zero Element
{0, 2, 4, 6, 8}	{0, 2, 4, 6}	{0, 2, 4}	{0, 2}	{0}	{ } or ∅
	{0, 2, 4, 8}	{0, 2, 6}	{0, 4}	{2}
	{0, 2, 6, 8}	{0, 2, 8}	{0, 6}	{4}
	{0, 4, 6, 8}	{0, 4, 6}	{0, 8}	{6}
	{2, 4, 6, 8}	{0, 4, 8}	{2, 4}	{8}
		{0, 6, 8}	{2, 6}
		{2, 4, 6}	{2, 8}
		{2, 4, 8}	{4, 6}
		{2, 6, 8}	{4, 8}
		{4, 6, 8}	{6, 8}

NULL SET

A set with no element is an empty set or null set. The symbol for empty set is { } or ∅.

Example:

1. Set T is the set of counting numbers between 1 and 2.
   T = { } or T = ∅

   
   

2. Set I is the set of months with 35 days.
   I = { } or I = ∅

   
   

3. Set M is the set of cars with 60 doors.
   M = { } or M = ∅

   
   

4. Set B is the set of flying castles.
   B = { } or B = ∅

   
   

5. Set E is the set of crying trees.
   E = { } or E = ∅

   
   

CARDINALITY OF SETS

The cardinal number of set A, denoted by n(A), is the number of elements in set A. Thus, in A = {1, 3, 5, 7}, n(A) = 4 because set A contains 4 elements.

Examples:

Find the cardinality of the following sets.

1. Set D is the set of vowels in English alphabet.
   Solution: D = {a, e, i, o, u}
   Answer: n(D) = 5

   
   

2. Set R is the set of letters in the word “difficulty”.
   Solution: R = {d, i, f, c, u, l, t, y}
   Answer: n(R) = 8

   
   

3. Set M is the set of odd numbers between 1 and 3.
   Solution: M = { } or M = ∅
   Answer: n(M) = 0

   
   

4. Set E is the set of letters in the word “survivor”.
   Solution: E = {s, u, r, v, i, }
   Answer: n(E) = 6

   
   

5. Set K is the set of counting numbers less than 5.
   Solution: K = {1, 2, 3, 4}
   Answer: n(K) = 4

   
   

What’s More

I. Find the cardinality of the following sets.

_____ 1. Set A is the set of days in a week. _____ 2. Set B is the set of letters in the word “recognition”. _____ 3. Set C is the set of even numbers less than 2. _____ 4. Set D is the set of odd numbers between 3 and 9. _____ 5. Set E is the set of factors of 12.

II. Tell whether each statement is True or False.

_____ 1. {3, 5, 7} ⊆ {1, 2, 3, … } _____ 2. {b, h, r, q} ⊆ {h, r} _____ 3. {3, 12, 5, 19} ⊆ {19, 3, 5, 12} _____ 4. {4} ⊆ {2, 4, 6, 10} _____ 5. ∅ ⊆ {1, 3, 5, 7}

What I Have Learned

To sum it up, let us complete the statements. Choose your answer from the box that best completes the statements below.

universal set | subset | cardinality of set | null set | { } or ∅ | union of set

1. A set with no element is an empty set or _____________________.

   
   

2. The number of elements in the set refers to _____________________.

   
   

3. The _____________________ U is the set that contains all objects under consideration.

   
   

4. If every element in A is also an element in B, then A is a _____________________ of B.

   
   

5. The symbol for empty set or null set is _____________________.

   
   

What I Can Do

I. TRUE or FALSE: Given the sets below, write true if the statement is correct and false if it is wrong. Write your answer in the space provided before the number.

S = {0, 1, 2, 3, 4, …, 10} V = {5, 10, 15, 20, 25} O = {d, a, y} I = {r, o, s, e} L = {3, 6, 9, 12} N = {roots, stem, leaves, flowers, fruits } G = {Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune}

_____ 1. The cardinality of Set G is 8. _____ 2. {5, 15, 25} is a subset of Set V. _____ 3. {8} is a subset of Set L. _____ 4. The cardinality of Set O is 7. _____ 5. The number of elements in Set N is 5. _____ 6. {s, u, n} is a subset of Set G. _____ 7. An empty set or { } is a subset of Set N. _____ 8. The cardinality of Set I is 10. _____ 9. {5, 6, 7, 8, 9} is a subset of Set S. _____ 10. One of the subsets of Set N and Set G is a ∅.

II. IDENTIFICATION: Identify the cardinality and the subsets of the following sets. You can use extra sheet of paper in listing the subsets of the given set.

1. Set A = {1, 8}
   n(A) = _____ Subsets: _____________________

   
   

2. Set B = {sun, moon, stars}
   n(B) = _____ Subsets: _____________________

   
   

3. Set C = {g, l, a, d}
   n(C) = _____ Subsets: _____________________

   
   

4. Set D = {2, 4, 6, 8}
   n(D) = _____ Subsets: _____________________

   
   

5. Set E = {green, orange, purple}
   n(E) = _____ Subsets: _____________________

   
   

Lesson 3: Union and Intersection of Sets and the Difference of Two Sets

In Arithmetic, we have learned the four fundamental operations that help us combine numbers. In sets, we are going to learn union and intersection of sets and the difference of two sets.

What’s In

Identify if each statement is true or false. Write your answer in the space provided. Given: U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

_____ 1. The universal set is {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. _____ 2. {2, 4, 6, 8, 10} is a subset of U. _____ 3. {0, 10} is a subset of U. _____ 4. Empty set { } is a subset of U. _____ 5. The cardinality number of set U is 10.

Notes to the Teacher

This activity will help the learners recall the concepts on Subsets, Universal Sets, Null Sets and Cardinality of Sets.

What’s New

Select your answer/s from the words inside the box.

What animals can live on land? Name them. What animals can live in water? Name them. What animals can live both in land and water?

[transcriber’s note: the word box is printed in two columns: dog, cat fish / frog, milk fish / cow, turtle]

What is It

OPERATION OF SETS

Name	Symbol	Definition
Union	∪	Is the set containing all elements that are in A or in B.
Intersection	∩	The set that consist of all elements that are both in A and B.
Difference	–	Is a set of elements in A that are not in B.

UNION OF SETS

The union of sets A and B, written as A ∪ B, is the set of elements that are members of A, or members of B, or members of both A and B.

Example:

1. If A = {1, 2, 3} and B = {1, 2, 4, 5, 6}, then A ∪ B = {1, 2, 3, 4, 5, 6}
2. If A = {a, b, c, d, e} and B = {a, e, i, o, u}, then A ∪ B = {a, b, c, d, e, i, o, u}
3. If A = {Monday, Tuesday, Wednesday, Thursday, Friday} and B = {Saturday, Sunday}, then A∪B = {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}

INTERSECTION OF SETS

The intersection of two sets A and B, written as A ∩ B, is the set of all elements common to both sets A and B.

Example:

1. If A = {1, 2, 3} and B = {1, 2, 4, 5, 6}, then A ∩ B = {1, 2}
2. If A = {a, b, c, d, e} and B = {a, e, i, o, u}, then A ∩ B = {a, e}
3. If A = {Monday, Tuesday, Wednesday, Thursday, Friday} and B = {Saturday, Sunday}, then A∩B = { } or ∅

DIFFERENCE OF TWO SETS

The difference of set A and B, written as A – B, is a set of elements in A that are not in B.

Example:

1. If A = {1, 2, 3} and B = {1, 2, 4, 5, 6}, then A – B = {3} while, B – A = {4, 5, 6}.
2. If A = {a, b, c, d, e} and B = {a, e, i, o, u}, then A – B = {b, c, d}, while B – A = {i, o, u}.
3. If A = {Monday, Tuesday, Wednesday, Thursday, Friday} and B = {Saturday, Sunday}, then A – B = {Monday, Tuesday, Wednesday, Thursday, Friday} while B – A = {Saturday, Sunday}.

What’s More

I. Perform the following operations on sets.

Given: A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} B = {2, 4, 6, 8, 10} C = {1, 3, 5, 7, 9}

1. A ∩ C = _____

   
   

2. B ∩ C = _____

   
   

3. A ∩ B = _____

   
   

4. A ∪ B = _____

   
   

5. B ∪ C = _____

   
   

6. A ∪ C = _____

   
   

7. A – C = _____

   
   

8. B – C = _____

   
   

9. A – B = _____

   
   

10. C – A = _____

    
    

II. Answer the following:

Given: Set X is the set of months in a year. Set Y is the set of months that ends in “ber”. Set Z is the set of months that has 31 days.

Find:

1. X ∩ Y = _____
2. Z ∩ X = _____
3. Z ∪ Y = _____
4. Y ∪ Z = _____
5. X – Z = _____

What I Have Learned

Fill in the blank with the correct word or symbol to make the statement TRUE.

1. The _____ of sets A and B, written as A ∪ B, is the set of elements that are members of A, or members of B, or members of both A and B.
2. The _____ of two sets A and B, written as A ∩ B, is the set of all elements common to both sets A and B.
3. The _____ of set A and B, written as A – B, is a set of elements in A that are not in B.
4. If A = {m, a, t, h} and B= {a, m}, then _____ = {a, m}.
5. If C = {English, Math, Science, Filipino, Values Education, TLE, Mapeh, Araling Panlipunan} and D = {Math, Science, English}, then _____ = {English, Math, Science, Filipino, Values Education, TLE, Mapeh, Araling Panlipunan}.
6. If O = {10, 20, 30, 40, 50} and P = {20, 40}, then _____ = {10, 30, 50}

What I Can Do

Here is another activity that allows you to apply what you learned about the operations on sets. Write your answer in the space provided.

1. If A = {a, b, c, d, e} and B = {a, c, f, g, h, i}, find:
   • (a) A ∪ B = _____
   • (b) A ∩ B = _____
   • (c) A – B = _____
2. If A = {2, 3, 4, 5}, B = {4, 5, 6, 7}, and C = {6, 7, 8, 9}, find:
   • (a) A ∪ B = _____
   • (b) B ∩ C = _____
   • (c) C – A = _____
3. If A = {4, 6, 8, 10, 12}, B = {8, 10, 12, 14}, C = {12, 14, 16} and D = {16, 18}, find:
   • (a) B ∪ D = _____
   • (b) A ∩ B = _____
   • (c) A – B = _____
4. Let X = {ballpen, crayon, pentel pen, pencil}, Y = {pencil, ballpen}, Z = {crayon}. Find:
   • (a) X ∪ Y = _____
   • (b) X ∩ Z = _____
   • (c) X – Y = _____
5. Given: Set R is the set of letters between a to j.
   Set S is the set of vowels.
   Set T is the set of letters from a to e.
   Find:
   • (a) R ∪ S = _____
   • (b) S ∩ T = _____
   • (c) T – S = _____

Assessment

Select the correct answer. Write the letter on a separate sheet of paper.

1. Which of the following is a well-defined set?

   • a. A set of good writers
   • b. A set of factors of 3.
   • c. A set of honest students in grade seven
   • d. A set small numbers

2. Which of the following is the symbol of a null set?

   • a. ∪ b. ∩ c. ⊆ d. ∅

3. Michelle listed the set of all letters in the word “serendipity” as shown below. What is wrong with this set?
   A = {s, e, r, e, n, d, i, p, i, t, y}

   • a. It uses commas.
   • b. It uses braces.
   • c. The objects in this set are not listed once.
   • d. A capital letter is used to represent this set.

4. Given the set of letters in the word “LOVE”. What is the cardinality of the given set?

   • a. 11 b. 8 c. 6 d. 4

5. What is the cardinality of {10, 20, 30, …, 80}?

   • a. 8 b. 10 c. 12 d. 14

6. The following are subsets of U= {5, 10, 15, 20, 25, 30, 35, 40, 45, 50}, EXCEPT?

   • a. {10, 20, 30, 50} c. {5, 10, 25}
   • b. {5, 10, 15, 20, 25, 37, 40} d. { }

7. How many subsets does G = {t, e, a, m} have?

   • a. 4 b. 12 c. 16 d. 20

8. Given A= {s, e, a, t} and B= {s, t, a, n, d}, find A∪B.

   • a. {s, e, a, t, n, d} b. {s, a, t} c. {n, d} d. {e}

9. Given F = {o, r, a, n, g, e} and G = {y, e, l, o, w}, find F∩G.

   • a. {o, r, a, n, g, e, y, l, w} c. {y, e, l, o, w}
   • b. {o, r, a, n, g, e} d. {e, o}

10. Given X = {bus, jeepney, taxi, tricycle} and Y = {tricycle}, find the difference of Y and X.

    • a. {bus, jeepney, taxi, tricycle} c. {tricycle}
    • b. {bus, jeepney, taxi} d. { }

11. List all positive even numbers less than or equal to 10.

    • a. {2, 4, 6, 8} c. {2, 4, 6, 8, 10}
    • b. {1, 3, 5, 7} d. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

12. Which of the following is a subset of F = {c, a, n, d, y}?

    • a. {c, a, n, d, y} b. {c, a, n, e} c. {0} d. {e}

*For numbers 13 – 15, use the following: A = { 0, 1, 2, 3, 4 } B = { 3, 5, 7, 8 } C = { 0, 2, 6, 8}

13. Find A ∪ B
    • a. {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} c. {3}
    • b. {0, 1, 2, 3, 4, 5, 7, 8} d. {0, 1, 2, 3, 4,3, 5, 7, 8}
14. Find B ∩ C
    • a. {0, 2, 3} b. {0, 2, 3, 6, 7, 8} c. {8} d. { }
15. Find A – C
    • a. {0, 1, 2, 4} b. {1, 3, 4} c. {3} d. { }

Additional Activities

Activity 1.1 Give what is asked

Do the following exercises.

I. Tell whether each of the following sets is well-defined or not.

1. The set of admiring places. _____
2. The set of all counting numbers _____
3. The set of workaholic teachers. _____
4. The set of letters in the word “father”. _____
5. The set of all factors of 36. _____

II. Give the cardinality of the following sets.

1. The set of counting numbers from 5 to 25 _____

   
   

2. The set of letters in the word “seven” _____

   
   

3. D = {1, 2, 3, 4, 5} _____

   
   

4. A = {m, o, d, u, l, e} _____

   
   

5. Y = {4, 8, 12, …, 36} _____

   
   

III. Let B = {2, 6}. List all the possible subsets of B.

IV. Answer the following. Write your answer in the space provided.

Given: If P = {1, 2, 3}, Q = {2, 3, 4}, R = {3, 4, 5}, and S = {4, 5, 6}

Find:

1. P ∪ Q _____
2. P ∪ R _____
3. Q ∪ R _____
4. Q ∪ S _____
5. P ∩ Q _____
6. P ∩ R _____
7. S ∩ P _____
8. Q – P _____
9. P – S _____
10. R – S _____

Answer Key

What I Know

1. c
2. b
3. d
4. c
5. b
6. b
7. d
8. a
9. c
10. d
11. a
12. d
13. a
14. c
15. b

[transcriber’s note: the key is printed upside down; a single printed letter “c” also appears in the margin beside the What I Know column]

Lesson 1

What’s More

1. not
2. well-defined
3. not
4. well-defined
5. well-defined
6. not
7. well-defined
8. not
9. well-defined
10. well-defined

What I Have Learned

1. e
2. b
3. c
4. d
5. a

What I Can Do

1. a
2. b
3. b
4. d
5. c
6. a
7. d
8. c [?]
9. d [?]
10. d [?]

[transcriber’s note: items 8 to 10 are hard to read in the upside-down print]

Lesson 2

What’s More

I.

1. n(A) = 7
2. n(B) = 8
3. n(C) = 1
4. n(D) = 2
5. n(E) = 6

II.

1. True
2. False
3. True
4. True
5. True

What’s In

Memory Check!

1. /
2. /
3. x
4. /
5. x

What I Can Do

I.

1. true
2. true
3. false
4. false
5. true
6. false
7. true
8. false
9. true
10. true

II.

1. n(A) = 2
   Subsets: {1, 8}, {1}, {8}, { } or ∅ [?]
2. n(B) = 3
   Subsets: {sun, moon, stars}, {sun, stars}, {sun, moon}, {moon, stars}, {sun}, {stars}, {moon}, { } or ∅

What I Have Learned

1. null set
2. cardinality of set
3. universal set
4. subset
5. { } or ∅

[transcriber’s note: the printed page number on this page is 22. The page is rotated 180 degrees and parts of it are hard to read, so uncertain readings are marked with [?].]

Lesson 2

What I Can Do

3. n(C) = 4

Subsets: {g, l, a, d}, {g, l, a}, {g, l}, {g}, { }, {g, l, d}, {g, a, d}, {g, a}, {g, d}, {l, a, d}, {l, a}, {l, d}, {a, d}, {l}, {a}, {d} [?]

4. n(D) = 4

Subsets: {2, 4, 6, 8}, {2, 4, 6}, {2, 4, 8}, {2, 6, 8}, {4, 6, 8}, {2, 4}, {2, 6}, {2, 8}, {4, 6}, {4, 8}, {6, 8}, {2}, {4}, {6}, {8}, { } [?]

5. n(E) = 3

Subsets: {green, orange, violet}, {green, orange}, {green, violet}, {orange, violet}, {green}, {orange}, {violet}, { }

Lesson 3

What’s In

1. true
2. true
3. false
4. true
5. true

What I Have Learned

1. union
2. intersection
3. difference
4. A ∪ B
5. C ∪ D
6. O − P

What’s More

I.

1. {1, 3, 5, 7, 9}
2. ∅ [?]
3. {2, 4, 6, 8, 10} [?]
4. {1, 3, 5, 7, 9} [?]
5. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} [?]
6. {1, 3, 5, 7, 9} [?]
7. {2, 4, 6, 8, 10} [?]
8. {2, 4, 6, 8, 10} [?]
9. {1, 3, 5, 7, 9} [?]
10. { } [?]

II.

1. {Sept, Oct, Nov, Dec}
2. {Jan, March, May, July}
3. {Jan, March, May, July} [?]
4. {Jan, Feb, March, April, May, June, July} [?]
5. {Feb, April, June, Aug, Sept, Oct, Nov, Dec} [?]

[transcriber’s note: the printed page number on this page is 23. The page is rotated 180 degrees.]

Lesson 3

What I Can Do

1. a. {a, b, c, d, e, f, g, h}
   b. {a, c}
   c. {b, d, e}

   
   

2. a. {2, 3, 4, 5, 6}
   b. {6, 7}
   c. {6, 7, 8, 9}

   
   

3. a. {8, 10, 12, 14, 16, 18}
   b. {8, 10, 12}
   c. {4, 6}

   
   

4. a. {ballpen, crayon, pentel pen, pencil}
   b. {crayon}
   c. {crayon, pentel pen}

   
   

5. a. {a, b, c, d, e, f, g, h, i, o, u}
   b. {a, c}
   c. {b, c, d}

   
   

Additional Activities

I.

1. not
2. well-defined
3. not
4. well-defined
5. well-defined

II.

1. 21
2. 4
3. 5
4. 6
5. 9

III.

1. {2, 6}
2. {2}
3. {6}
4. { }

IV.

1. {1, 2, 3, 4}
2. {1, 2, 3, 4, 5}
3. {2, 3, 4, 5}
4. {2, 3, 4, 5, 6}
5. {2, 3}
6. {3}
7. {3}
8. {4}
9. {1, 2, 3}
10. {3}

Assessment

1. b
2. d
3. c
4. d
5. a
6. b
7. c
8. a
9. d
10. d
11. d
12. a
13. a
14. d
15. b

[transcriber’s note: the printed page number on this page is 24.]

References

K TO 12 GRADE 7 LEARNING MODULE IN MATHEMATICS (Q1 – Q2). (2014, March 11). Retrieved from https://www.slideshare.net/lhoralight/k-to-12-grade-7-learning-material-in-mathematics-q1q2

Oronce, O. & Mendoza, M. (2015). e – math 7: Worktext in Mathematics. (pp. 2 –9). Quezon City, Philippines: Rex Book Store, Inc.

[transcriber’s note: the printed page number on this page is 25.]

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