SETS
1. Definition of a Set
A set is a well-defined collection of distinct objects. The objects in a set are called its
elements or members.
The phrase well-defined means that it must be possible to decide clearly whether a given
object belongs to the set or not.
Sets are usually denoted by capital letters such as A, B, C, etc., and their elements are
denoted by small letters such as a, b, c, etc.
If an object x is an element of a set A, we write x ∈ A. If x is not an element of A, we
write x ∈
/ A.
Examples of Sets
1. Vowels in the English alphabet
V = {a, e, i, o, u}
2. Natural numbers less than 5
N = {1, 2, 3, 4}
3. Days in a week
D = {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}
4. Even numbers between 1 and 10
E = {2, 4, 6, 8}
Examples of Not a Set
• Collection of beautiful flowers
• Collection of good students
Methods of Representing a Set
1. Description Method
A = {first five natural numbers}
2. Roster Form
A = {1, 2, 3, 4, 5}
3. Set Builder Form
A = {x | x is a natural number and x ≤ 5}
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1. Definition of a Set
A set is a well-defined collection of distinct objects. The objects in a set are called its
elements or members.
The phrase well-defined means that it must be possible to decide clearly whether a given
object belongs to the set or not.
Sets are usually denoted by capital letters such as A, B, C, etc., and their elements are
denoted by small letters such as a, b, c, etc.
If an object x is an element of a set A, we write x ∈ A. If x is not an element of A, we
write x ∈
/ A.
Examples of Sets
1. Vowels in the English alphabet
V = {a, e, i, o, u}
2. Natural numbers less than 5
N = {1, 2, 3, 4}
3. Days in a week
D = {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}
4. Even numbers between 1 and 10
E = {2, 4, 6, 8}
Examples of Not a Set
• Collection of beautiful flowers
• Collection of good students
Methods of Representing a Set
1. Description Method
A = {first five natural numbers}
2. Roster Form
A = {1, 2, 3, 4, 5}
3. Set Builder Form
A = {x | x is a natural number and x ≤ 5}
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