Types -Of-Sets Empty Set, Singleton Set, Equivalent Sets, Equal Sets, Finite Set , Infinite Set, Subsets, Super Set , Proper Set, Universal Set, Complement Set .
The types of sets are empty set, singleton set, equivalent sets, equal sets, finite set , infinite set, subsets, super set , proper set, universal set, complement set .
Empty set or Null set
A set which doesnot contain any set is called as Empty set or Null set or Void set. It is denoted by ‘∅’ and it is read as phi. In roster form empty set is denoted by {}. The cardinality of null set is always 0.
For example:
The set set of
whole number less than 0.
The set of even prime number less than 2.
Singleton set
a set which contain only one element is called as singleton set. The cardinality of singleton set is always 1.
For example:
The set of
even prime numbers. A = {2}, | A | = 1
A = {x|x is
a whole number less than 1}
S = {x|X is a natural number, x*x=4}
Finite set
A set which has a definite number of elements is called as finite set. The cardinality of finite set is always definite.
For
example:
The set of
colours in the rainbow .
The set of
natural number less than 15.
P={2,3,4,5,6,7,8,9}
· Infinite set
A set which has infinite number of elements is called as infinite set. The cardinality of infinite set is always infinite.
For
example:
Set of
natural numbers.
Set of
prime numbers
Set of
whole numbers
Set of
integers.
· Equivalent sets
Two sets A and B are equivalent when their cardinality is same. The symbol for denoting equivalent set is ‘↔’
For example
:
A={1,2,3,4,5}
and B ={a,e,i,o,u} here, n(A) =n(B)=5 A↔B
X={2,4,6,8,10}
and G={1,2,3,4,5}
V={a,v,c,d}
and K={q,w,e,r}
· Equal sets
Two sets A and B are said to be equal sets when they contains same elements. Every element which belongs to set A also belongs to set B.
For example:
A = {
q,w,e,r} and B ={ e,w,q,r}
S={c,v,b,n}
and G ={b,v,n,c}
Z={1,3,4,2}
and L = {1,2,3,4}
· Subset
A subset of a set A is a set that contains only elements from set A, but may not contain all the elements of set A. ‘⊆’ this symbol is used to represent the subset .
If B is a
subset of set A we can write as : B ⊆ A
If A is a
subset of set B we can write as : A ⊆ B
Some properties
of subsets are:
Every set is a
subset of itself. Symbolically,
A A, B
B.
Empty set is a
subset of every set .
For example:
A = {1,2,3}
The subsets of set
A are :
B={}
C={1}
N={2}
H={3}
V={1,2}
M={1,3}
K={2,3}
A={1,2,3}
If we have cardinality of the given set is ‘n’ then
the set have ‘2ⁿ’ subsets.
Here, we have cardinality of set is 3 so, set A has 2³
= 8 subsets.
· Super set
Whenever set A is a subset of set B then set B is a superset and we can write it as B⊇A
Symbol ‘⊇’ is used
to denote “ is a super set of “.
For example :
A={a,s,c,f,v} and
B={a,b,c,d,……………..,y,z}
Here A is a subset
of B i.e. A ⊆ B.
B is a superset of
A i.e. B⊇ A
· Proper subset
if And B are two sets then, A is called as proper set of B if A ⊆ B but not B⊇ A i.e. A ≠B . The symbol ‘⊂’ is used to denote proper subset.
For example:
A
={1,2,3,4} here, n(A) = 4
B =
{1,2,3,4,5} here, n(B) = 5
A ⊂ B means A is a proper subset of B.
If we have cardinality of the given set is ‘n’ then
the set have ‘2ⁿ -1 ’ proper subsets .
· Power set
The collection of all subsets of set A is called as power set of a set A. It is denoted by P(A). In P(A) , every element is a set.
For example
:
A={p,q}
P(A) ={ {},
{q},{p}, {p,q} }
If we have cardinality of the given set is ‘n’ then
the power set of the set have ‘2ⁿ’ elements .
Here, n(A)
= 2
n[P(A)] =
2² = 4
· Universal set
A universal set is a set that contains all the elements of other given sets is called a universal set . The symbol to denote universal set is ‘U’.
U={1,2,3,4,5,6,7,8,9,10}
A
={1,2,3,4,5}
B={1,2,3,4,5,6,7}
C={1,2,3}
M={1,2,5,6}
Here u is
the universal set for set A, B, C and M
· Complement set
A complement set is relative to the universal set. The complement of set A contains all the elements present in universal set except the elements which are in set A. The complement of set A is denoted as A’.
For example
U={1,2,3,4,,56,7,8,9}
A={1,3,5,7,9}
A’={2,4,6,8},
#complement set of set A.
Operations-on-sets Union-Intersection-Difference-Complement and The Laws Of The Operations
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