Venn Diagram for Different Situation




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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