Closed intervals | Empty set | equal sets | Equivalent sets | Finite and infinite set | Set | Singleton set | Types of sets
Types of sets
TYPES OF SETS
a) Empty set
A set is said to be empty or null or void set if it has no element and it is denoted by Φ
In Roster method is Φ denoted by { }.
Example
{ x : x ∈ R, x2=-2 }=Φ
{ x : x ∈ N, 5<x<6 }=Φ
D={ x : x2=4, x is odd } Then D is the empty set. Because equation x2=4 is not satisfied by any odd value of x. So it has no elements.
b) Singleton set
When set contain single element. That type of set is called singleton set.
Example
Set A={x : x ∈ N, x2=9 } is a singleton set. Because it has single element {3}.
c) Finite and infinite set
A set which is empty or consists of a definite number of elements is called finite otherwise, the set is called infinite.
Example
a) Let S be the set of solutions of the equation
X2–9= 0. Then S is finite.
b) Let G be the set of points on a line. Then G is infinite.
b) Let G be the set of points on a line. Then G is infinite.
d) Equivalent sets
Two finite sets A and B are equivalent if thier cardinal numbers are same. i.e, n(A) =n(B)
NOTE
Cardinal number of finite set is the number of elements in the set and is denoted by n(A), n(B), n(C)………. So on.
Example
A={4, 5, 9, 6 , 7 } B={8, 3, 2, 4, 1}
Set A and B are equivalent set because cardinal number is equal n(A) = n(B).
c) Equal sets
Two set A and B are said to be equal if every element of A is a member of B and every element of B is a member of A
If set A and B are equal, we write A=B and A≠B when A and B are not equal.
Example
A={ 1, 5, 6, 9 } B={6, 9, 1, 5 }, A=B
Set A and B are equal set.
NOTE
All equivalent set is equal set but all equal set is not a equivalent set
“THANK YOU”
Please visit again