The document defines and provides examples of different types of sets: 1. Empty/null sets contain no elements. Singleton sets contain only one element. Finite sets contain a finite number of elements, while infinite sets are not finite. 2. Subsets contain elements of another set. Proper subsets are subsets that are not equal to the original set. Power sets are the set of all subsets of a given set. 3. Examples are given of empty, singleton, finite, infinite, equivalent, equal, subset, and proper subset sets. Cardinal numbers represent the number of elements in a set.

1. TYPES OF SET
Presented by,
M.Mahapoorani,
Mathematics.

2. SET:
A set is a collection of
collection of well defined
objects.

3. Examples:
 The collection of all colours in a
rainbow.
 The collection of prime numbers.
 The collection of all books in a District
Central Library.

5. Types of set:
1.Empty set or Null set:
For example :
• The set of all integers between 1 and 2.
• The set of squares with five sides.
A set consisting of no element.
denoted by {} or Φ

7. Singleton set:
A set has only one element.
For example:
 The set of all even prime numbers.
 The set {0} , {4} , {5},etc.

9. A B
Which one is a singleton set?

10. Finite set:
A set with finite elements.
For example:
 The set of family members.
 x = {1,2}

11. Infinite set:
 A set which is not finite.
For example:
 The set of all points on a line.
 Set of all integers.

12. The drops of water in ocean is an infinite set.

13. Cardinal number of a set:
 The number elements in a set is called
a cardinal number of the set.
 The set is finite.
 denoted by n(A).

14. For example:
 If A = {1,2,3,4,5}
Then n (A) = 5
 if A = {x : 3 < x <5, x£ N}
Here A= 4
then n(A) =1.

15. Equivalent sets:
 The two finite sets A and B contain
the same number of elements.
 If A and B are equivalent sets, then
n(A) = n(B)
 written as A ≈ B.

16. For example:
Let
A = { ball, bat}
B = { history, geography}
Here A is equivalent to B.
since n(A) = n(B) = 2.

17. A B
≈
Here A is equivalent to B.

18. Equal sets:
 If two sets are equal, they
contain exactly the same
number of elements.
 written as A = B

19. ``````````In other words,
 every element of A is also an
element of B.
 every element of B is also an
element of A.

20. For example,
let A ={ 1,2,3,4}
B ={4,3,2,1}
Then A and B are equal sets, since
A and B contain exactly the same
elements.

21. A B
Here A and B are equal sets.

22. Subset:
 Every element of A is also an
element of B.
 if A is a subset of B, then
n(A) ≤ n(B).

23. For example:
 {1} is a subset of {1,2,3}
 {a,b} is a subset of {a,b,c,d,e,f}
 If A ={a ,b }.
then the subsets of A are Φ, {a},{b},
{ a, b}.

24. Natural numbers
Whole numbers
Integers

25. Proper subset:
1. A is a subset of B .
2. A ≠ B.
then A is called a proper subset of B.
3.Every element of A is also an
element of B but there exist at least one
element in B but not in A.
For example:
let A = {1,2,5 } and B={1,2,3,4,5}.
Then A is a proper subset of B.

26. For example:
 {1,2,3} is a subset of {1,2,3} but
not a proper subset of {1,2,3}
 {1,2,3} is a proper subset of
{1,2,3,4} . since the element 4 is not in
the first set.

27. Problem:1
If A = {a,b,c,d} then
Write the proper set
of A .
Problem:2
If X ={p,q,r,s} and
Y={p,q,r,s,t}. Is it
Correct to say X is a
Proper subset of Y ?

28. Power set:
 the set of all subset of a set.
 denoted by P(A).
 subset Power set
A collection of
some of the
elements of a
set.
The collection of
all subsets of a
set.

29. Let A = {2,3}
Then subset of A are Φ,{2},{3},{2,3}.
therefore P(A)= {Φ,{2}{3},{2,3}}.

30. What is P(A)?