Evaluating Algebraic Expression

1

Control No: _______________

SLK for _Mathematics 7
QUARTER 1 WEEK 1

I.PRELIMINARIES

Competency

Illustrates well-defined sets, subset, universal sets, null set,
cardinality of sets, union, and intersections of sets and the different of
two sets.

Objectives

1. Define a well-defined set.
2. Illustrate a subset, universal set, null set, cardinality of set, union,
intersection, and difference of two sets.
3. Appreciate the importance of a set.

Topic/
Subject
Matter

Illustration of Sets

Textbook

Learner’s Module in Grade 7 Elizabeth R. Aseron, Angelo D. Armas,
pages 1-10
E – math 7: Worktext in Mathematics by Oronce, O. & Mendoza, M.
(pp. 2 –9).

Materials

ballpen, crayon/coloring material

Copyrights

DepEd Talisay City

Total Points 70 points
Date

September 13 – 17, 2021

II. CONTENT MAP

Illustration of

Sets

Subsets

UniversalSet

Null Set

Cardinality of sets

Union

Intersection

Difference of two sets

2

III. CONTENT NOTES

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

Example:

A set of mountains

A set of books

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

3. The set of all multiples of 5.

M = {𝑟𝑒𝑑, 𝑦𝑒𝑙𝑙𝑜𝑤, 𝑏𝑙𝑢𝑒}

Y = {5, 10, 15, … }

2. The set of all even numbers. 4. The set of letter in the word “arrange”.

E = { 2, 4, 6, … }

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

*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.

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}

3

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;





2. O = {red, blue, yellow}
The possible subsets are;






3. S = {3, 6, 9, 12}
The possible subsets of set S are;

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 = ∅

Two elements

One element

Zero element

{1, 2}

{1}

{ } or ∅

{2}

Three elements

Two elements

One element

Zero element

{red, blue, yellow}

{red, blue }

{ blue }

{ } or ∅

{red, yellow }

{yellow }

{ blue, yellow }

{red}

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

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, 𝑜 }
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

OPERATION OF SETS

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}

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.

5

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}.

6

IV. ACTIVITIES
Activity 1 (Illustration of sets)

Competency: Illustrates well-defined sets, subset, universal sets, null set, cardinality
of sets, union, and intersections of sets and the different of two sets.

Date: September 13, 2021

HPS: 20 points

Directions: I. Draw a if it is a well-defined set, a if it is not.Write your
answer on the ANSWET SHEET provided.

____________1. The set of all BNHS 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 male student in a class

____________8. The set of all multiples of 5

____________9. A group of good writers

____________10. Nice people in your class

II. TRUE or FALSE: Given the sets below, write true if the statement is correct
and false if it is wrong. Write your answer on the ANSWER SHEET provided.

S = {0, 1, 2, 3, 4, ... , 10} V = {5, 10, 15, 20, 25}

O = {d, a, y}

L = {3, 6, 9, 12} N = {roots, stem, leaves, flowers, fruits}

I = {r, o, s, e}

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 ∅.

7

Activity 2 (Illustration of sets)
Competency: Illustrates well-defined sets, subset, universal sets, null set, cardinality
of sets, union, and intersections of sets and the different of two sets.
Date: September 14, 2021

HPS: 10pts.

Directions: Answer the following. Write your answer on the ANSWER SHEET
provided.

Given:

If P = {1, 2, 3}, Q = {2, 3, 4},

R = {3, 4, 5}, and S = {4, 5, 6}

Find:

1. P ∪ Q

6. P ∩ R

2. P ∪ R

7. S ∩ P

3. Q ∪ R

8. Q – P

4. Q ∪ S

9. P – S

5. P ∩ Q

10. R – S

8

Activity 3
Competency: Illustrates well-defined sets, subset, universal sets, null set, cardinality
of sets, union, and intersections of sets and the different of two sets.

Date: September 14, 2021

HPS: _20pts._

THE HIDDEN MESSAGE

Directions: What is the hidden message written below despite this pandemic
outbreak of corona virus? To answer, shade the elements of the result of the
difference of two sets on each of the following number.

1. A= { c, o, r, o, n, a}
B= {v, i, r, u, s}
A-B=___________

c

c

c

o

v

v

o

o

n

R

r

n

A

a

a

2. A = {a, e, i, o, u}
B = {a, b, c, d ,e}
A-B=___________

i

i

i

a

o

e

a

o

e

a

u

e

a

u

e

A= {2,4,6,8,10}
B = {1,3,5,7,9}
A-B=___________

2

2

2

4

1

8

4

6

8

6

3

10

6

7

10

4. A = {w, e, a, r}
-B = {m, a, s, k}
A-B=___________

w

a

w

w

e

w

m

e

s

m

r

k

a

r

k

5. A = { r,e,p,a,c,k}
B = {r,e,l,i,e,f}
A-B=___________

p

p

p

a

r

e

a

a

c

l

f

c

k

k

k

6. A = {f, a, k, e}
B = {n, e, w, s}
A-B=___________

f

f

f

a

n

k

a

f

k

a

w

k

a

s

k

7.A = {1,2,3…10}
B = {2,4,6…10}
A-B=___________

1

1

1

3

2

4

3

7

9

5

6

8

5

10

10

8. A = {4,8,12…40}
B = {2, 4, 8…64}
A-B=___________

12

20

24

12

4

8

28

36

36

28

16

32

40

40

40

V. EVALUATION:

Competency: Illustrates well-defined sets, subset, universal sets, null set, cardinality
of sets, union, and intersections of sets and the different of two sets.

Date: September 13-17, 2020

HPS: 15 pts.

9

Directions: Choose the letter of the best answer. Write the chosen letter on your
ANSWER SHEET.

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

a. A set of good writers

c. A set of honest students in grade seven

b. A set of factors of 3.

d. A set small numbers

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

a. 

b. Ս

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. c. The objects in this set are not listed once.

b. It uses braces.

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. { }

10

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. {

}

VI. ENRICHMENT

In math there are sets of numbers, equations, and other factors that can be used
in daily life for calculations whether it is to calculate the cost of something, income
earnings, or other calculations based on circumstances in one's life.

•Medicine

Chinese medicine uses 'sets' to complete things they believe to be out of balance.
One of the most important things to be balanced in Chinese culture is the body. If
one part of the body is off balance, it will cause an illness; therefore, there is a 'set'
of two things that provides this equality. It can be considered Yin and Yang in
Asian cultures.

•Science

In science there are 'sets' of data. Data sets are a series of numbers obtained
through an experiment. These sets do not have to be equal or balanced. They are
just a series of numbers recorded based on the experiment and then later used to
interpret the results of the experiment. They may also be calculated using
mathematical sets to obtain relevant statistics such as the median.

•Education

There are school sets like flashcards, study tools, etc. That provide one with
helpful tools to learn. These 'sets' are used in daily life to fulfill one's need for
knowledge.

11

VII. ANSWER KEY

VIII. REFERENCES

Elizabeth R. Aseron, Angelo D. Armas, Allan M. Canonigo, Ms Jasmin T. Dullete, Flordelize R.
Francisco,PH.D., Ian June L. Garces, Ph.D.,Eugenia V. Guerra, Phoebe V. Guerra, Almira D. Lacsina,
Rhett Anthony C. Latonio, Lambert G. Quesada, Ma. Cristy R. Reyes, Rechilda P. Villame, Debbie
Marie B. Verzosa, Ph.D.,and Catherine P. Vistro-Yu, Ph.D 2013. Mathematics – Grade 7 Learner’s
Material. Pasig City.
Fernando B. Orines, Catalina B. Manalo, Josephine L. Suzara, Jesus P. Mercado 2012. Next Century
Mathematics 7. Quezon City
https://lrmds.deped.gov.ph/detail/7436
Orlando A. Oronce : Marilyn O. Mendoza . E - Math Worktext in Mathematics: REX Publishing

House, Inc., 2015

Prepared by:
Name: _Mary Grace R. Alberca__
School: _BULACAO NHS___

Activity 1

Activity 2

I. 1. 😊

II. 1. True

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

2. 😐

2. True

2. {1,2,3,4,5} 7. { }

3. 😐

3. False

3. {2,3,4,5}

8. {4}
4. 😊

4. False

4. {2,3,4,5,6} 9. {1,

2,3}
5. 😐

5. True

5. {2,3] 10. {3}

6. 😊

6. False

7. 😊

7. True

8. 😊

8. False

9. 😐

9. True

c c c

o v v

o o n

R r n

A a a

i i i

a o e

a o e

a u e

a u e

2 2 2

4 1 8

4 6 8

6 3 10

6 7 10

w a w

w e w

m e s

m r k

a r k

p p p

a r e

a a c

l f c

k k k

f f f

a n k

a f k

a w k

a s k

1 1 1

3 2 4

3 7 9

5 6 8

5 10 10

12 20 24

12 4 8

28 36 36

28 16 32

40 40 40

12

VIII. FEEDBACK NOTES Math 7 Q1 W1

LEARNER’S FEEDBACK

_________________________________________

_________________________________________

_________________________________________

_________________________________________

_________________________________________

_________________________________________

_________________________________________

_________________________________________

_________________________________________

_________________________________________

_________________________________________

_________________________________________

PARENTS’/GUARDIANS’ FEEDBACK

________________________________________________________

________________________________________________________

________________________________________________________

________________________________________________________

________________________________________________________

________________________________________________________

________________________________________________________

________________________________________________________

________________________________________________________

________

13

IX. ANSWER SHEET Math 7 Q1 W1

Control No: _______________

Name: __________________________________ Grade & Sec.: ______________
Contact No:______________

School: _________________________

Subject : Mathematics

Teacher: ____________________

Activity 1
Directions: I. Draw a if it is a well-
defined set, a if it is not.

1. ___________

6. ___________

2. ___________

7. ___________

3. ___________

8. ___________

4. ___________

9. ___________

5. ___________

10.

___________

II. TRUE or FALSE: Given the sets below,
write true if the statement is correct and
false if it is wrong.

1. ___________

6. ___________

2. ___________

7. ___________

3. ___________

8. ___________

4. ___________

9. ___________

5. ___________ 10. ___________

Activity 2

1. ______________6. ___________

2. _____________ 7. __________

3. ______________ 8. __________

4. ______________ 9. __________

5. ______________10. __________

Evaluation

1. _______

9. ___________

2. ________

10. ___________

3. ________

11. ___________

4. ________

12. ___________

5. ________

13. ___________

6. ________

14. ___________

7. ________

15. ___________

8. ________

14

Activity 3THE HIDDEN MESSAGE
Directions: What is the hidden message written below despite this pandemic
outbreak of corona virus? To answer, shade the elements of the result
of the difference of two sets. (Use one color of crayon in shading)

1.

c

c

c

o

v

v

o

o

n

R

r

n

A

a

a

2.

i

i

i

a

o

e

a

o

e

a

u

e

a

u

e

3.

2

2

2

4

1

8

4

6

8

6

3

10

6

7

10

4.

w

a

w

w

e

w

m

e

s

m

r

k

a

r

k

5.

p

p

p

a

r

e

a

a

c

l

f

c

k

k

k

6.

f

f

f

a

n

k

a

f

k

a

w

k

a

s

k

7.

1

1

1

3

2

4

3

7

9

5

6

8

5

10

10

8.

12

20

24

12

4

8

28

36

36

28

16

32

40

40

40