3. Kinds of Sets…
Infinite or Uncountable Set
when the elements of a set is uncountable, the set is known as infinite or
uncountable set.
means the last member of a set is unknown.
A = { 1 , 2 , 3 , 4 ……….. }
B = { The number of stars }
C = { The set of all Even numbers }
Overlapping or Joint Set.
if at least one member of set A is also a member of set B, then set A and B are overlapping sets.
A = { 1 , 2 , 3 , 4 , 5 } and B = { 2 , 4 , 6 , 7 }
A and B are overlapping sets because { 2 , 4 } are common.
4. Kinds of Sets
Disjoint Set
if two sets having no element in common is known as disjoint sets.
A = { 1 , 3 , 5 , 7 , 9 } , B = { 2 , 4 , 6 , 8 , 10 }
set A and B are disjoint sets because there is no element in both the sets is common.
Equal Sets
Two sets are said to be equal if and only if every element of A also belongs to B and
vice versa.
Symbolically it can be written as A = B
A = { 1 , 2 , 3 } , B = { 2 , 3 , 1 } now A ⊆ B and B ⊆ A
So A = B
5. Kinds of Sets
Equivalent Sets
When the cardinality of two sets are equal then the sets are said to be
equivalent.
A = { 1 , 2 , 3 } , B = { a , b , c }
The cardinality of set A and B is 3 so both sets are equivalent.
Power Set
For set A, a collection of all subsets of A is called the power set of A.
denoted by P (x) and formulated by 2𝑛.
A = { 1 , 2 , 3 } then P(A) = 2𝑛
=> 23
= 8 members
P (A) = { ∅ , 1 , 2 , 3 , {1,2} , {1,3} , {2,3} , {1,2,3} }
6. Set Operations
Union of two sets
For any two sets A and B, the union of A and B is a set of all elements which are
members of set A or set B or both. Denoted by ∪.
Let A = { 1 , 2 , 3 , 4 , 5 } and B = { 2 , 3 , 6 , 7 }
Union of set A and B is
A ∪ B = { 1 , 2 , 3 , 4 , 5 } ∪ { 2 , 3 , 6 , 7 }
A ∪ B = { 1 , 2 , 3 , 4 , 5 , 6 , 7 }
Here in union if a member comes 2 times so we will write the member as one time in
the union operation. As in the above example members 2 and 3 are coming two times
and answer we have written once.
7. Union of two sets
A = { a , c , e , f , g , h } , B = { b , d , f, i , m , n}
C = { a , e , i , o , u }
Find A ∪ B , B ∪ C , A ∪ C
Solution>>
A ∪ B = { a , c , e , f , g , h } ∪ { b , d , f, i , m , n}
A ∪ B = { a , b , c , d , e , f , g , h , i , m , n}
B ∪ C = { b , d , f, i , m , n} ∪ { a , e , i , o , u }
B ∪ C = { a , b , d , e , f, i , m , n , o , u }
A ∪ C = { a , c , e , f , g , h } ∪ { a , e , i , o , u }
A ∪ C = { a , c , e , f , g , h , i , o , u }
8. Set Operations
Intersection of two sets
The intersection of A and B is the set of all elements that is belong to both A and B.
Means common in both sets.
A ∩ B={x | x ∊ A ˄ x ∊ B}
Let A = { 1 , 2 , 3 , 4 , 5 } B = { 2 , 4 }
A ∩ B = { 1 , 2 , 3 , 4 , 5 } ∩ { 2 , 4 }
A ∩ B = { 2 , 4 }
A = { 1 , 2 , 3 , …….. 10 } , B = { 1 , 3 , 5 , 7 , 9 } C = { 2 , 4 , 6 , 8 , 10 }
A ∩ B = { 1 , 2 , 3 , …….. 10 } ∩ { 1 , 3 , 5 , 7 , 9 }
A ∩ B = { 1 , 3 , 5 , 7 , 9 }
9. Intersection of two sets…
A ∩ C = { 1 , 2 , 3 , …….. 10 } ∩ { 2 , 4 , 6 , 8 , 10 }
A ∩ C = { 2 , 4 , 6 , 8 , 10 } A = { Red , Yellow , Blue , White }
B = { Red , Blue , Green} A ∩ B = {Red , Yellow , Blue , White }
∩ { Red , Blue , Green}
A ∩ B = { Red , Blue }
Let A = { 3, 4, 5, 6 }, B = { 5, 6, 7 }, C = { 7, 8, 9 }
A ∩ B ={ 3, 4, 5, 6 }∩ { 5 , 6 , 7 }
A ∩ B ={ 5, 6 }
A ∩ C ={ 3, 4, 5, 6 }∩ { 7 , 8 , 9 }
A ∩ C ={ } no element is common.
10. Set Operations
Difference of two sets
If A and B are any two sets then the difference of B in A is the set of all elements in
A which are not in B. It is denoted by A ─ B ,
A-B= AB={x | x ∊ A ˄ x ∉ B}
A = { 1 , 2 , 3 , 4 , 5 } , B = { 2 , 4 }
A – B = ?
A = { a , b , c , d } , B = { b , d , e , f }
A – B = { a , b , c , d } – { b , d , e , f }
A – B = ?
B – A = ?
11. Set Operations
Complement of a set
The complement of a set is the all members which is not included in that set. The
complement of a set we will obtain by subtracting all the members of that set from
the universal set.
(set) c= U – ( set ) For example A`= U – ( A ) here we are
taking the complement of set A that’s why we subtract set A from the universal set.
B`= U – ( B )
S`= U – ( S )
A`={x | x∉ A ˄ x∊U}
A ∪ A`=U A ∩A`= ∅
U
A`
A
12. Complement of a set…
U = { 1 , 2 , 3 , 4 ……… 10 }
A = { 1 , 3 , 5 , 7 , 9 } , B = { 2 , 4 , 6 , 8 , 10 }
B` = U – ( B )
A` = ?
C = { a , b , c , d } ,
U = { a , b , c , d , e , f , g }
C`=?
