This document defines key concepts about sets including: - A well-defined set is one whose elements can be specifically identified. An example of a well-defined set given is the set of numbers between 10 and 20. - The cardinality of a set refers to the number of elements in the set. Several examples of sets and their cardinalities are provided such as the set of vowels in the English alphabet which has a cardinality of 5. - An empty set is a set with no elements, denoted by {} or ø. Two examples of empty sets are given. - Sets can be classified as finite if their elements are countable, or infinite if their elements cannot be counted as they extend infinitely.

2. A set is well-defined it its elements can be specifically identified.
An empty set is a set with no elements.
The cardinality of a set is the number of elements in the set.
Sets can be classified as finite or infinite.
finite sets – elements are countable
infinite sets – cannot be counted since it extends infinitely

3. Identifying A Well-defined And
Not Well-defined Sets

4. Example 1. The set of counting numbers between 10 and 20.
A = {11, 12, 13, 14, 15, 16, 17, 18, 19}
It is a well-defined set because we can specifically list the elements of this
set.
Example 2. The set of nice animals.
This is not a well-defined set because we cannot specifically identify the nice
animals. What is nice animal to one person may not be nice to another
person.

5. Cardinality
The cardinality of a set is the number of elements in the set. If A is a set, the
cardinality of set A is denoted by n(A).
Set Cardinality
1. A = {11, 12, 13, …20} n(A) = 10
2. B = {x / x is a day in a week } n(B) = 7
3. C = {x / x is a vowel in the
English alphabet}
n(C) = 5
4. D = {5, 10, 15, 20, 25, 30} n(D) = 6
If the cardinality of a set is zero, then the set is empty.

6. Empty Set
An empty set is a set with no elements . It is denoted by the
symbol { } or ø . The cardinality of an empty set is 0.
Study these examples.
1. A = { x / x is an odd number divisible by 2}
A = {} or ø
2. B = { x / x is a month of a year beginning with R }
B = ø

7. A set can be classified as finite or infinite.
Study these examples:
1. A = {1, 2, 3, 4, 5, } is a finite set.
2. B = {2, 6, 6, 8, … 30} is a finite set.
3. C = {1, 3, 5, 7, …} is an infinite set.
4. D = {x / x is a counting number greater than 10} is an
infinite set.

8. THANK YOU