Mathematics 7 The Language of Sets

1. The Language of
SETS
Mr. Carlo Justino J. Luna
CONRADO P. MACAPINLAC,SR. HIGH SCHOOL

2. To Define A Set

3. WAYS TO DEFINE A SET
ROSTER METHOD (Listing all the
elements)
Examples: A={10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
B={a, e, i, o, u}
SET-BUILDER NOTATION (Describing the
elements)
Examples: C={x|x is one of the first ten multiples of 10}
D={x|x is a vowel in the English alphabet}

4. Write each set using roster method.
1. Distinct letters in the
word ADMIRABLE
Answer:
{A, D, M, I, R, B, L, E}

5. Write each set using roster method.
2. Colors of the Philippine
flag
Answer:
{blue, red, yellow, white}

6. Write each set using roster method.
3. Months of the year
ending with “ber”
Answer:
{September, October, November,
December}

7. Write each set using roster method.
4. The set of whole
numbers from 2 to 5
Answer:
{2, 3, 4, 5}

8. Write each set using set-builder notation.
1. {a, b, c, d, e, f, g, h, I,
j}
Answer:
{x|x is one of the first ten letters
of the alphabet}

9. Write each set using set-builder notation.
2. {5, 10, 15, 20, 25, 30,
35}
Answer:
{x|x is one of the first seven
multiples of 5}

10. Write each set using set-builder notation.
3. {M,O, N, K, E, Y}
Answer:
{x|x is a distinct letter in the
word MONKEY}

11. Write each set using set-builder notation.
4. {1, 3, 5, 7, 9, 11, 13,…}
Answer:
{x|x is an odd number}

12. Write each set using set-builder notation.
5. {Saturday, Sunday}
Answer:
{x|x is a day in the weekends}

13. Comprehension Check
Write each of the
following using
ROSTER METHOD.

14. Number 1
The days of the week
starting with the
letter T

15. Number 2
The set of whole
numbers between
10 and 15

16. Number 3
The set of even whole
numbers less than 13

17. Number 4
The set of Grade 7
subjects

18. Number 5
The set of primary
colors

19. Comprehension Check
Write each of the
following using SET-
BUILDER NOTATION.

20. Number 1
{2, 4, 6, 8, 10, 12, 14,
16, 18, 20, … }

21. Number 2
{Monday, Tuesday,
Wednesday, Thursday,
Friday}

22. Number 3
{Luna, Agcanas, Cortez,
Famorcan, Mallari,
Cortez, Mendoza}

23. Number 4
{1, 3, 5, 7, 9, 11, 13,
15, 17, 19}

24. Number 5
{February}

25. ELEMENTS
of a Set
and
WELL-DEFINED
Sets

26. ACTIVITY: Are You a Member of the Set?
Stand up if you are a member of this set.
1. Set of students who were born in June
2. Set of students love pizza
3. Set of students who like to play basketball
The students who stand up in each item would
comprise the members of that set

27. Suppose the set of students who were born in
June is named set A.
Jenny is born in June.
So “Jenny ∈ A” means Jenny is an element
of Set A.
Jed is born in February.
So “Jed ∉ A” means Jed is an not an
element of Set A.

28. EXAMPLE: Fill in each blank with ∈ or ∉.
Set A = {even numbers between 0 and 10}
A = {2, 4, 6, 8}
Set B = {letters of the alphabet between c and j}
B = {d, e, f, g, h, i}
1. 2 __ A
2. 5 __ A
3. 12 __ A
4. b __ B
5. g __ B
6. e __ B
∈
∉
∉
∉
∈
∈

29. EXAMPLE: Fill in each blank with ∈ or ∉.
Set A = {months of the year ending in “ber”}
A = {September, October, November, December}
1. January __ A
2. October __ A
3. December __ A
4. August __ B
∈
∉
∉
∈

30. In a set-builder notation, some
situations exist that make it difficult
to determine whether an object
belongs to the set.
For instance, if we are interested in
“pretty girls in the Philippines”, it
might be difficult to determine if a
particular girl belongs to the set.

31. A girl who is pretty for someone may
not be pretty for another.
As they say, beauty is in the eye of the
beholder.
Since beauty is subjective, the set
“pretty girls in the Philippines” is not
WELL-DEFINED.

32. WELL-DEFINED SET
Definition:
A set is WELL-DEFINED if it is
clear whether a particular
object belongs to the set.

33. EXAMPLE: State whether the collection is a
well-defined set.
1. {a subject in Grade 7}
2. {a popular actor}
3. {a favorite fruit}
4. {a student in your class}
5. {a teacher in your school}
YES
NO
NO
YES
YES