Venn Diagram for Different Situation

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Venn diagram for different situation :

The shaded region represents the relation between the sets.

The shaded region represents the relation between the sets.

1) A’ -----> Complement of set A.


2) B’ -----> Complement of set B.


3) A ∪ B


4) (A ∪ B )’ -------> Complement of union set.


5) A ∩ B


6) ( A ∩ B)’ -------> Complement of intersection set.


7) ( A – B) -----> Difference of the two sets.


Example :

From the given Venn diagram,find :
1) Set A
2) Set B
3) A ∪ B
4) A ∩ B
5) A'
6) B'
7) A - B
8) B - A
9) ( A ∪ B)'
Solution :
ξ = { 1,2,3,4,5,6,7,8,9,10,11,12 }
1) A = { 1,2,3,4,5,6}

2) B = { 4,5,6,7,8,9}

3) A ∪ B = { 1,2,3,4,5,6,7,8,9}

4) A ∩ B = { 4,5,6}

5) A' = { 7,8,9,10,11,12}

6) B' = { 1,2,3,10,11,12 }

7) A - B = {1,2,3}

8) B - A = { 7,8,9}

9) ( A ∪ B)' = {10,11,12}
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Practice

1) Draw a Venn diagram for each of the following :
1) A'∩ B'.
2) A'.

2) Use Venn diagram : In a school, there are 20 teachers who teach Mathematics or English. Of these, 12 teach Mathematics and 4 teach both English and Mathematics. How many teach English only?

3) A and B are two sets. n(A) = 17,n(B) = 23 and n(A ∩ B).
Find n(A ∪B).
Set Theory

• Sets
• Representation of Set
• Cardinal Number
• Types of Sets
• Pairs of Sets
• Subset
• Complement of Set
• Union of the Sets
• Intersection of Sets
• Operations on Sets
• De Morgan's Law
• Venn Diagrams
• Venn-diagrams for sets
• Venn diagram for different situations
• Problems on Intersection of Two Sets
• Problems on Intersection of Three Sets
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