A set is a collection of distinct objects that can be defined as belonging or not belonging to that set. A set is denoted with a capital letter, such as set A = {1, 2, 3}. The elements within a set are enclosed in braces. A set is considered well-defined if any given object can be clearly identified as either belonging or not belonging to that set. Examples of well-defined sets include sets of past presidents, basketball team players, or days of the week. Sets can be defined through listing elements, describing characteristics of elements, or using rules to specify elements.

1. BASIC
CONCEPTS OF
SET
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2. A set is a group or collection of
distinct objects. A set is well-
defined if a given object can be
identified as belonging to that
set or not.

3. We denote each set by a
capital letter. Thus, set A =
{1, 2, 3} is well-defined. Each
member of a set is an
element of the set.

4. 4
Note that when elements of a
set are enumerated, they are
enclosed in braces. Using the
same example above, we say
that 3 is an element of A, but a
4 is not an element of A.

5. 5
Definition.
A set is any collection of
distinct objects.
A set is well-defined if a given
object can be defined as
belonging to a set or not.

6. Here are the examples.
1. The set P of past
presidents of a country.
2. The set B of players of a
basketball team.

7. 3. The set C of members of
a committee.
4. The set D of the days of
the week.
5. The set M of the months
of the year.

8. 8
The following are examples of
ill-defined sets.
1. The set P of the ten prettiest
girls in a school.
2. The set T of the most
talkative students in class I-

9. 9
3. The set N of the most
popular TV shows.
4. The set K of the most
popular actresses.

10. 10
In the first example, given any
girl in a school, can you tell if
she belongs to P or not? If you
say that Josie is one of the ten
prettiest girls in a school, not
all may agree with you.

11. 11
Why are sets T, N, K not well-
defined?
A set be defined using the
following methods; listing or
roster, description, or rule or
property defining method or
set-builder notation.

12. 1. Listing or roster method
Examples
a. V = {a, e, i, o, u}
b. M = {January, February, March, May,
June}

13. 2. Description Method
Examples
a. V = {vowels in the English
alphabet}
b. D = { The students in Class I-C}

14. 14
3. Rule or property defining method or
set-builder notation
Examples
a. O = {n|n is an odd number from 1 to
99 inclusive}
b. P = {p|p is a past president of the
Philippine Republic}