# CLASS-8FIND THE SETS FROM VENN DIAGRAM

Find the following sets from the Venn Diagram

Find the following sets from the Venn diagram –

1) U,  2)   A,   3)   B,   4)  C,    5)   A’ ,   6)   B’ ,   7)   C’ ,   8) ∩ B ,   9)  B  ∩  C ,   10)   A  ∩  C ,     11) A – B ,   12)  B – C ,    13)   A – C ,    14)   (A – B)’ ,   15)   ( B  ∩  C )’

1)   U

Answer) As per the given condition of Venn Diagram, we can find that –

U  =  { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 }

2)   A

Answer) As per the given condition of Venn Diagram, we can find that –

A = { 3, 4, 5, 7, 8, 9, 10 }

3)   B

Answer)  As per the given condition of Venn Diagram, we can find that –

B = { 1, 2, 3, 4, 5, 6, 12 }

4)   C

Answer) As per the given condition of Venn Diagram, we can find that –

C  = { 3, 5, 7, 9, 11, 13, 15 }

5)   A’

Answer)  As per the given condition of Venn Diagram, we can find that –

A’ = U – A =  { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 } – { 3, 4, 5, 7, 8, 9, 10 }

=  { 1, 2, 6, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 }

6)   B’

Answer) As per the given condition of Venn Diagram, we can find that –

B’ = U – B

=  { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 } – { 1, 2, 3, 4, 5, 6, 12 }

=   { 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19 }

7)   C’

Answer) As per the given condition of Venn Diagram, we can find that –

C’ = U – C

=   { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 } – { 3, 5, 7, 9, 11, 13, 15 }

=   { 1, 2, 4, 6, 8, 10, 12, 14 }

8)   ∩ B

Answer) As per the given condition of Venn Diagram, we can find that –

∩ B   =  { 3, 4, 5, 7, 8, 9, 10 }  ∩  { 1, 2, 3, 4, 5, 6, 12 }

=   { 3, 4, 5 }

9)  B ∩ C

Answer) As per the given condition of Venn Diagram, we can find that –

∩ C  =  { 1, 2, 3, 4, 5, 6, 12 } ∩ { 3, 5, 7, 9, 11, 13, 15 }

=  { 3, 5 }

10)   A ∩

Answer) As per the given condition of Venn Diagram, we can find that –

∩ C  =  { 3, 4, 5, 7, 8, 9, 10 } ∩ { 3, 5, 7, 9, 11, 13, 15 }

=  { 3, 5, 7, 9 }

11)   A – B

Answer) As per the given condition of Venn Diagram, we can find that –

A – B  =  { 3, 4, 5, 7, 8, 9, 10 } – { 1, 2, 3, 4, 5, 6, 12 }

=  { 7, 8, 9, 10 }

12)  B – C

Answer) As per the given condition of Venn Diagram, we can find that –

B – C =  { 1, 2, 3, 4, 5, 6, 12 } – { 3, 5, 7, 9, 11, 13, 15 }

=  { 1, 2, 4, 6, 12 }

13)   A – C

Answer) As per the given condition of Venn Diagram, we can find that –

B – C =  { 3, 4, 5, 7, 8, 9, 10 }  – { 3, 5, 7, 9, 11, 13, 15 }

=  { 4, 8, 10 }

14)   (A – B)’

Answer) As per the given condition of Venn Diagram, we can find that –

A – B =  { 3, 4, 5, 7, 8, 9, 10 } – { 1, 2, 3, 4, 5, 6, 12 }

=  { 7, 8, 9, 10 }

(A – B)’  =  U - (A – B)

= { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 } - { 7, 8, 9, 10 }

=  { 1, 2, 3, 4, 5, 6, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 }

15)  ( B ∩ C )

Answer) As per the given condition of Venn Diagram, we can find that –

C  =  { 3, 4, 5, 7, 8, 9, 10 }   { 3, 5, 7, 9, 11, 13, 15 }

=   { 3, 5, 7, 9 }

Example.3)  If  B = { 1, 2, 3 } , B A = { 2 }  and A – B = { 4, 5, 6 }, then fill the elements in the Venn Diagram, also tabulate the elements of the sets A, B – A  and  B U A

Answer) Let, us first fill the elements of B A and A – B, let us fill the elements of B that are not contained in B A, these elements are 1 & 3, now from the venn diagram, A = { 2, 4, 5, 6 } ,

B – A = { 1, 2, 3 } – { 2, 4, 5, 6 }  =  { 1, 3 } , and

B U A = { 1, 2, 3 } U { 2, 4, 5, 6 }  = { 1, 2, 3, 4, 5, 6 }

Here we can observe that, in this picture set A is defined by Green color, set B is defined by Red color and the common portion of set A & B are described by purple color.