2. Definition of a set
Notation
Representation of Sets
Types of Sets
3. Definition
A set is a well defined collection of different objects.
Ex: Colours in the rainbow.
Days of the week.
Elements
The object in a set are called its elements.
4. NOTATION
Set - Capital letters
Elements – Small letters
V = { a,e,i,o,u}
5. Symbols
The symbol “∈” denotes
Ex:
V= { a,e,i,o,u}
a ∈ V – a belongs to V
b∉ V – b does not belong to V
6. Representation of sets
There are three methods widely used to represent a
set. They are,
i) Roster Method
ii) Rule Method
iii) Description Method
7. Roster Method
A set is given by listing elements in a
row, separated by commas and
enclosed in set bracket is called
Roster Method.
Ex: A = { 1,2,3,4,5}
8. Rule method
The method in which the set is described by stating
the common properties of all elements is known as Rule
method.
Ex: A is a set of positive integers less than 10.
A= {x / x is an even positive integer less than 10}
9. Description Method
A set may be represented by means of a
precise statement only in words, is known as
Description method.
Ex: A is a set of any three water animals.
10. Types of sets
Empty set Equal sets
Singleton set Equivalent sets
Finite set Disjoint sets
Infinite set Overlapping sets
Universal set Subsets
11. Empty set
A set having no element is called empty set. It is also
called as an empty set or void set. It is denoted by {} or ∅
Ex: Set of all persons who have four eyes
12. Singleton set
A set which only one element is called a singleton
set.
Ex:
1) The set of months which have less than 30 days.
A = {Feb}
2) E= {n / n ∈ Z and 3<n<5}
E= {4}
13. Finite set
If set contains countable number of elements, it
is known as finite set.
Ex: The set of all fishes in a fish tank.
G= {2,4,6,8,10}
14. Infinite set
If a set contains unlimited number of elements,
it is known as infinite set.
Ex:
The set of all fishes in the ocean.
15. Equal sets
If two sets contain the same elements and same
number they are said to be equal.
Ex: A= { a,b,c,d} B= {d, a, b,c} A and B are equal
sets.
16. Equivalent sets
IF the cardinalities of two sets are same, they
are called equivalent sets.
A = { Ram, Ravi, Rajesh}
B = { 4,5,6}
In sets A and B, there are three elements.
17. Disjoint sets
Two sets A and B are called disjoint if A and B
have no elements in common.
Ex:
A= {1,3,5,7} and B= {a, e,i,o,u}
A ∩ B = ∅
A and B are disjoint sets.
18. Overlapping sets
Two sets that have atleast one common element
are called overlapping sets.
Ex: A= {1,2,3,4,5} and B= {5,6,7,8,9}
A ∩B = {5}
19. Universal set
A universal set is a set which contains all the
elements of other sets, including its own
elements. It is usually denoted by “U”.
Ex: A {1, 2, 3, 4,5} B= { 6,7,8,}
U = { 1,2,3,4,5,6,7,8,9,10}
20. Subsets
If the set ‘A’ is called the subset of set ‘B’ if
every element ‘ A’ is also an element of B.
In other words, the set A is contained inside the
set of B.
Ex: A {1,2} B= {1,2,3,4}
