How to find the difference of sets using Venn diagram?
The difference of two subsets A and B is a subset of U, denoted by A – B and is defined by
A – B = {x : x ∈ A and x ∉ B}.
Let A and B be two sets. The difference of A and B, written as A  B, is the set of all those elements of A which do not belongs to B.
Thus A – B = {x : x ∈ A and x ∉ B} or A – B = {x ∈ A : x ∉ B}.
Clearly, x ∈ A – B
⇒ x ∈ A and x ∉ B
In the adjoining figure the shaded part represents A – B.
Similarly, the difference B – A is the set of all those elements of B that do not belongs to A.
Thus, B – A = {x : x ∈ A and x ∉ B} or A – B = {x ∈ B : x ∉ A}.
In the adjoining figure the shaded part represents B – A.
In particular, A – B = ∅ if A ⊂ B and A – B = A if A ∩ B = ∅.
The subset of A – B is also called the complement of B relative to A.
The difference A – B can be expressed in terms of the complement as A – b = A ∩ B’.
Properties of difference of sets:
1. A – (B ∩ C) = (A – B) ∪ (A – C)
2. A – (B ∪ C) = (A – B) ∩ (A – C)
Solved example to find the difference of sets using Venn diagram:
1. If A = {2, 3, 4, 5, 6, 7} and B = {3, 5, 7, 9, 11, 13}, then find (i) A – B and (ii) B – A.
Solution:
According to the given statement; A = {2, 3, 4, 5, 6, 7} and B = {3, 5, 7, 9, 11, 13}
(i) A – B
= {2, 4, 6}
(ii) B – A
= {9, 11, 13}
2. Given three sets A, B and C such that: A = {x : x is a natural number between 10 and 16}, B = {set of even numbers between 8 and 20} and C = {7, 9, 11, 14, 18, 20}.
Find the difference of sets using Venn diagram:
(i) A – B
(ii) B – C
(iii) C – A
(iv) B – A
Solution:
According to the given statement
A = {11, 12, 13, 14, 15}
B = {10, 12, 14, 16, 18}
C = {7, 9, 11, 14, 18, 20}
`(i) A – B
= {Those elements of set A which are not in set B}
= {11, 13, 15}
(ii) B – C
= {Those elements of set B which are not in set C}
= {10, 12, 16}
(iii) C – A
= {Those elements of set C which are not in set A}
= {7, 9, 18, 20}
(iv) B – A
= {Those elements of set B which are not in set A}
= {10, 16, 18}
`● Set Theory
● Finite Sets and Infinite Sets
● Problems on Intersection of Sets
● Problems on Complement of a Set
● Problems on Operation on Sets
● Venn Diagrams in Different Situations
● Relationship in Sets using Venn Diagram
● Union of Sets using Venn Diagram
● Intersection of Sets using Venn Diagram
● Disjoint of Sets using Venn Diagram
● Difference of Sets using Venn Diagram
8th Grade Math Practice
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