Sets can be defined by listing elements between curly braces or using a property that defines the elements. There are several standard sets like the set of natural numbers N and real numbers R. Sets are either finite if they contain a definite number of elements, or infinite if the elements cannot be listed. An empty set contains no elements, while a singleton set contains exactly one element. The cardinal number of a set is the number of distinct elements it contains. Two sets are disjoint if they share no common elements, and equal if they contain the same number and types of elements. A set A is a subset of set B if all elements of A are also elements of B.

1. SETS

2. Objectives
•Introduction to Sets
•Types of Sets

3. SET
A set is a well defined collection of objects, called the "elements" or
"members" of the set.
A specific set can be defined in two ways-
1. If there are only a few elements, they can be listed individually, by
writing them between curly braces '{ }' and placing commas in between. E.g.-
A = { a, e, i, o,u}
2. The second way of writing set is to use a property that defines elements
of the set.
e.g. T= { y | y is odd and 0 < x < 100}
If a is an element of set A, it can be written as e e A‘
If y is not an element of A, it can be written as ‘y € A1

4. SPECIAL SETS
Standard notations used to define some sets:
a. N- set of all natural numbers N= { 1,2,3,….}
b. Z- set of all integers,… Z = {. ..,-3,-2,-
1,0,1,2,3,…}
c. W. set of all Whole W = {
0,1,2,3,4,5,……….}
d. R- set of all real numbers
e. C-set of all complex numbers

5. TYPES OF SETS

7. FINITE SET
A set which contains a definite number of
elements is called a finite set. Empty set is
also called a finite set.
For example:
The set of all colors in the rainbow.
T = {a,e,i,o,u}
P = {2, 3, 5, 7, 11, 13, 17.......97}

9. INFINITE SET
The set whose elements cannot be listed,
i.e., set containing never-ending elements
is called an infinite set.
For example:
• Set of whole numbers1
e.g
W= { 0,1,2,3,4 ….}
Set of all possible even
numbers
E={0,2,4,,6,8,10,12,14,.}

11. EMPTY SETS
• A set which does not contain any
elements is called as Empty set or Null or
Void set. Denoted by 0 or { }
• example:
(a) The set of whole numbers less than 0.
(b) Clearly there is no whole number less than 0.
Therefore, it is an empty set.
(c) Set of integers between 1 and 2 {}

13. SINGLETON SET
A singleton set is a set containing exactly
one element.
Example: Let B = {x : x is a even prime
number}
Here B is a singleton set because there is
only one prime number which is even, i.e., 2.
A = {x : x is neither prime nor composite}
It is a singleton set containing one element,
i.e., 1.

14. CARDINAL NUMBER OF A SET
• The number of distinct elements in a
given set A is called
the cardinal number of A. It is denoted by
n(A).
• For example:
A {x : x e N, x < 5}
A = {1, 2, 3, 4}
Therefore, n(A) = 4
B = set of letters
in the word
ALGEBRA
B = {A, L, G, E,
B, R} Therefore,
n(B) = 6

15. DISJOINT SETS
• Two sets A and B are said to be
disjoint, if they do not have any element in
common.
• For example:
A = {x : x is a even number}
B = {x : x is a odd number}.
Clearly, A and B do not have any element
in common and are disjoint sets.

16. EQUAL SETS
Two sets A and B are called equal if they
have equal numbers and similar types of
elements.i. This implies,
A=B
For e.g. If A={1, 3, 4, 5, 6}
B={4, 1, 5, 6, 3} then both Set A and B are equal.

17. SUBSET
If every element of a set A is also an element of set B, we say set A
A £ B
Example-
If A={1,2,3,4,5,6} and
B={1,2,3,4}
Then B £ A

18. Home Work
Why empty set is called a
set????