The document defines some key concepts about sets: - A set is well-defined if its elements can be specifically identified. An example of a well-defined set is the set of numbers between 10 and 20. - The cardinality of a set refers to the number of elements in the set. Finite sets have countable elements while infinite sets extend infinitely. - An empty set is a set with no elements, denoted by {} or ø, and has a cardinality of 0.

2. A set is well-defined if 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, 4, 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