This document introduces key concepts about sets. It defines a set as a well-defined group of objects that share a common characteristic. It discusses subsets and the universal set. Important notations and symbols used to describe sets are explained, including roster notation, verbal descriptions, and set builder notation. Examples are provided to illustrate these concepts and notations. Activities at the end ask the reader to identify well-defined sets, list subsets, provide verbal descriptions of sets, and write sets in different notations.

1. SET: AN INTRODUCTION

2. Answer the following questions.
1. How many groups are there?
2. Does each object belong to a group?
3. Is there an object that belongs to more than one
group? Which one?

3. The groups are called sets for as
long as the objects in the group
share a characteristic and are
thus, well-defined.

4. Consider the following set:
set of two legged
creatures
set of tall buildings
set of large numbers

5. IMPORTANT TERMS TO REMEMBER
 A set is a well-defined group of objects,
called elements that share a common
characteristic.
Example:
3 of the objects belong to the set of head
covering or simply hats.
(ladies hat, baseball cap, hard
hat)

6. IMPORTANT TERMS TO REMEMBER
 The set A is a subset of set B if all elements of
A are also elements of B.
Example:
the even numbers 2, 4 and 12 all belong to the
set of whole numbers. Therefore, the even
numbers 2, 4, and 12 form a subset of the set of
whole number.
 A is a proper subset of B if A does not contain
all elements of B.

7. IMPORTANT TERMS TO REMEMBER
 The universal set U is the set that
contains all objects under consideration.
 The null set ∅ is an empty set. The null set
is a subset of any set.
 The cardinality of a set A is the number of
elements contained in A.

8. NOTATIONS AND SYMBOLS
 Uppercase letters will be used to name sets
 Lower case letters will be referred to any
element of a set
Example:
let H be the set of all objects that cover
or protect the head. We write
H= {ladies hat, baseball cap, hard
hat}
This is the listing or roster method of naming the

9. NOTATIONS AND SYMBOLS
 The symbol ∅ or { } will be used to refer to an
empty set.
 If set A is a subset of set B, then we write
A ⊆ B. We also say that B contains the set A
and write it as B ⊇ A. If A is a proper subset
of B, then we write A ⊂ B.
 The cardinality of a set A is written as n(A).

10. NOTATIONS AND SYMBOLS
Three ways in which we can describe a set.
These are the following
1.) The Roster Notation or Listing Method
 This is a method describing a set by
listing each element of the set inside the
symbol{ }. In listing the elements of the set,
each distinct element is listed once and the
order of the elements does not matter.
Examples:
A= {1,2,3,4} B= {p. h. i, l, n, e. s}

11. NOTATIONS AND SYMBOLS
2.) The Verbal Description Method
It is a method of describing a set in words.
We can describe the sets named in no.1 as
follows.
Examples:
1. Set A is the set of counting numbers less
than 5.
2. Set B is the set of letters in the word
“Philippines.”

12. NOTATIONS AND SYMBOLS
3.) The Set Builder Notation (Rule Method)
It is a method that lists the rules that
determines whether an object is an element
of the set rather than the actual elements.
We can describe the sets in no. 1, in set
builder notation as follows.
Examples:
1. A= {x|x is a counting number less than 5}
read as “ the set A is the set of all x’s such
that x is a counting number less than 5.”
2. B={x|x is a letter in the word "Philippines"}

13. ACTIVITY 2: “KNOW MORE ABOUT ME”
Which of the following are well defined sets?
1.) The set of all the days in a week beginning with
the letter “T”.
2.) The set of all difficult questions in a test.
3.) The set of girls in your class.
4.) The set of all resorts in Lupao.
5.) The set of all active teachers in the school.
6.) The set of all integers more than -3.
7.) The set of all beautiful flowers in the park
8.) The set of big cities in the Philippines.
9.) The set of subjects in grade 7.
10.) The set of animals in the zoo.

14. ACTIVITY 3: “MORE ABOUT SETS”
Do the following exercises.
1. Let B={ 1, 3, 5, 7, 9}. List all the possible
subsets of B.
2. Write a verbal description for each of the
following sets.
a. D= {1, 3, 5, 7,… }
b. E={>. ?, @,…, A }
c. F={4, 8, 12, 16,…,92 }
3. Give at least one well-defined set.

15. ASSIGNMENT: “PROJECT TRANSFORMATION”
Write each of the following sets in Roster form
and Set-builder notation.
1. Set of all natural numbers which can divide
24 completely.
2. Set of odd numbers between 20 and 35.
3. Set of even natural numbers less than 25.
4. Set of letters used in the word
‘PHILIPPINES’
5. Set of names of the first five months of a