# Union of Sets
The Union of two sets A and B is the set C which consists of all those elements which are
either in A or in B ( including those which are in both ). In symbols, we write :
Some Properties of the Operation of UNION :
(i) A ∪ B = B ∪ A ( Commutative law )
(ii) ( A ∪B ) ∪ C = A ∪ ( B ∪ C ) ( Associative law )
(iii) A ∪ 𝜱 = A ( Law of Identity element, 𝜱 is the identity of U )
(iv) A ∪ A = A ( Idempotent law )
(v) U ∪ A = U ( Law of U )
# Intersection of Sets
The intersection of two sets A and B is the set of all those elements which belongs to both
A and B. Symbolically, we write :
A ∩ B = { x : x ∈ A or x ∈ B }
The intersection of two sets can be represented by a Venn Diagram as shown below :
The Shaded portion in the above figure indicates the intersection of A and B.
Some Properties of the Operation of INTERSECTION :
(i) A ∩ B = B ∩ A ( Commutative law )
(ii) ( A ∩ B ) ∩ C = A ∩ ( B ∩ C ) ( Associative law )
(iii) 𝜱 ∩ A = 𝜱 , U ∩ A = A ( Law of 𝜱 and U )
(iv) A ∩ A = A ( Idempotent law )
The Union of two sets A and B is the set C which consists of all those elements which are
either in A or in B ( including those which are in both ). In symbols, we write :
A ∪ B = { x : x ∈ A or x ∈ B }
The union of two sets can be represented by a Venn Diagram as shown below :
(i) A ∪ B = B ∪ A ( Commutative law )
(ii) ( A ∪B ) ∪ C = A ∪ ( B ∪ C ) ( Associative law )
(iii) A ∪ 𝜱 = A ( Law of Identity element, 𝜱 is the identity of U )
(iv) A ∪ A = A ( Idempotent law )
(v) U ∪ A = U ( Law of U )
# Intersection of Sets
The intersection of two sets A and B is the set of all those elements which belongs to both
A and B. Symbolically, we write :
A ∩ B = { x : x ∈ A or x ∈ B }
The intersection of two sets can be represented by a Venn Diagram as shown below :
Some Properties of the Operation of INTERSECTION :
(i) A ∩ B = B ∩ A ( Commutative law )
(ii) ( A ∩ B ) ∩ C = A ∩ ( B ∩ C ) ( Associative law )
(iii) 𝜱 ∩ A = 𝜱 , U ∩ A = A ( Law of 𝜱 and U )
(iv) A ∩ A = A ( Idempotent law )
(v) A ∩ ( B ∪ C ) = ( A ∩ B ) ∪ ( A ∩ C ) ( Distributive law )
# Difference of Sets
The difference of the sets A and B in this order is the set of elements which belongs to A
but not to B . Symbolically, we write :
A - B and read as " A minus B " .
The Difference of two sets can be represented by a Venn Diagram as shown below :
The Shaded portion in the above figure indicates the Complement of A or A'.
# Difference of Sets
The difference of the sets A and B in this order is the set of elements which belongs to A
but not to B . Symbolically, we write :
A - B and read as " A minus B " .
The Difference of two sets can be represented by a Venn Diagram as shown below :
The Shaded portion in the above figure indicates the Difference of A and B.
# Complement of Set
Let U be the universal set and A a subset of U . Then the complement of A is the set of all
elements of U which are not the elements of A . Symbolically, we write :
A' to denote the complement of A with respect to U . Thus ,
A' = { x : x ∈ U and x ∉ U } . Obviously A' = U - A
The Complement of set can be represented by a Venn Diagram as shown below :
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