# CLASS-8INTERPRETING A VENN DIAGRAM

INTERPRETING A VENN DIAGRAM

In the Venn Diagram shown alongside, the rectangle representing the universal set U contains the elements 7, 9, 11, 1, 3, 6, 8, 10.

So, universal set U  = { 1, 3, 6, 7, 8,  9, 10, 11 } and n(U) = 8

The closed region in the rectangle representing the set A contains the elements  1, 3, 7, 9, 11 while that representing the set B contains 1, 3, 6, 8, 10.

A = { 1, 3, 7, 9, 11 } and  n(A) = 5

B = { 1, 3, 6, 8, 10 } and  n(B) = 5

A U B = { 1, 3, 7, 9, 11 } U { 1, 3, 6, 8, 10 } = { 1, 3, 6, 7, 8, 9, 10, 11 }  and  n(A U B) = 8

And  A B = { 1, 3, 7, 9, 11 } { 1, 3, 6, 8, 10 }

= { 1, 3 } and n (A B) = 2

And,  A B =  { 7, 9, 11 }  and  n (A B) = 3

Now, B – A =  { 6, 8, 10 }  and  n ( B – A ) = 3

A’ = ( U – A ) = { 1, 3, 6, 7, 8,  9, 10, 11 } – { 1, 3, 7, 9, 11 }

= { 6, 8, 10 }

And  n (A’) = 3

B’ = ( U – B )

= { 1, 3, 6, 7, 8,  9, 10, 11 } – { 1, 3, 6, 8, 10 } = { 7, 9, 11 }

And  n (B’) = 3

(A U B)’ =  U - (A U B)

= { 1, 3, 6, 7, 8,  9, 10, 11 } - { 1, 3, 6, 7, 8, 9, 10, 11 } =  φ

And  n (A U B)’ =  φ

(A B)’ =  U - (A B)

{ 1, 3, 6, 7, 8,  9, 10, 11 } – { 1, 3 } = { 6, 7, 8, 9, 10, 11 }

And, n (A B)’ = 6