A set is a collection of unique objects that have something in common. Sets are denoted with capital letters and elements with lowercase letters. Elements are listed within curly braces. There are two methods for indicating a set - listing all elements or describing the rule elements follow using braces. Describing elements is useful for large sets to avoid listing every item. Sets can be defined precisely by listing elements or generally by describing the type of elements.

1. SET
A set is a collection of objects that have something in common or follow a rule. The
objects in the set are called its elements. Set notation uses curly braces, with
elements separated by commas. So the set of outwear for Kyesha would be listed
as follows:
A = {coat, hat, scarf, gloves, boots}, where A is the name of the set, and the braces
indicate that the objects written between them belong to the set.
Every object in a set is unique: The same object cannot be included in the set
more than once.
Let's look at some more examples of sets.
Example 1: What is the set of all fingers?
Solution: P = {thumb, index, middle, ring, little}
Note that there are others names for these
fingers: The index finger is commonly referred to
as the pointer finger; the ring finger is also
known as the fourth finger, and the little finger is
often referred to as the pinky. Thus, we could
have listed the set of fingers as:
P = {thumb, pointer, middle, fourth, pinky}
Example 2: What is the set of all even whole
numbers between 0 and 10?
Solution: Q = {2, 4, 6, 8} Note that the use of the
word between means that the range of
numbers given is not inclusive. As a
result, the numbers 0 and 10 are not
listed as elements in this set.
Example 3: Eduardo was in art class when the teacher
wrote this on the chalkboard: In fine arts,

2. primary colors are sets of colors that can be
combined to make a useful range of
colors. Then she asked the class: What is the
set of primary colors?
Solution: Eduardo answered: red, blue and yellow.
Angie answered: We can use set notation to
list the set of all primary colors. Kyesha went
to the chalkboard and wrote:
X = {red, blue, yellow}
The teacher said: Good work everyone. This
is a nice combination of art and math!
In examples 1 through 4, each set had a different number of elements, and each
element within a set was unique. In these examples, certain conventions were
used.
The following conventions are used with sets:
 Capital letters are used to denote sets.
 Lowercase letters are used to denote elements of sets.
 Curly braces { } denote a list of elements in a set.
So for examples 1 through 4, we listed the sets as follows:
1. A = {coat, hat, scarf, gloves, boots}
2. P = {thumb, index, middle, ring, little}
3. Q = {2, 4, 6, 8}
4. X = {red, blue, yellow}
These sets have been listed with roster notation. Roster notation is a list of
elements, separated by commas, enclosed in curly braces. The curly braces are
used to indicate that the elements written between them belong to that set. Let's
look at some more examples of sets listed with roster notation.
Example 4: Let R be the set of all vowels in the English alphabet.
Solution: R = {a, e, i, o, u}

3. Example 5: Let G be the set of all whole numbers less than ten.
Solution: G = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
Example 6: Let T be the set of all days in a week.
Solution: T = {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}
Example 7: Let X be the set of odd numbers less than 12.
Solution: X = {1, 3, 5, 7, 9, 11}
Example
8:
Let Y be the set of all continents of the world.
Solution:
Y = {Asia, Africa, North America, South America, Antarctica, Europe,
Australia}
There are times when it is not practical to list all the elements of a set. In this case,
it is better to describe the set. The rule that the elements follow can be given in the
braces. For example,:
R = {vowels} means Let R be the set of all vowels in the English alphabet.
This is especially useful when working with large sets, as shown below.
A = {types of triangles}
G = {letters in the English alphabet}
J = {prime numbers less than 100}
M = {state capitals in the US}
When describing a set, It is not necessary to list every element in that set. Thus,
there are two methods for indicating a set of objects: 1) listing the elements and 2)
describing the elements. We will distinguish between these two methods in
examples 10 and 11 below.
Example 9: What is the set of all letters in the English alphabet?

4. Listing elements:
D = {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}
Describing
elements:
D = {letters in the English alphabet}
Example 10: What is the set of all states in the Unites States?
Solution: R = {all states in the US}
In example 10, set D has 26 elements, so it is easier to describe its elements than
to list them. Similarly, in example 11, setR has 50 elements, so it is easier to
describe its elements.
Summary: A set is a collection of objects that have something in common or
follow a rule. The objects in the set are called its elements. Curly
braces are used to indicate that the objects written between them
belong to a set. Every object in a set is unique. It is not necessary to
list every object in the set. Instead, the rule that the objects follow can
be given in the braces. We can define a set by listing its elements or
by describing its elements. The latter method is useful when working
with large sets.