CLASS-8
FIND THE SETS FROM 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) A ∩ 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)   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 }     

          =   { 3, 4, 5 }

 9)  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 }

        =  { 3, 5 }

 10)   A ∩ C 

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

A ∩ 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 –

B ∩ 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 }