Formulas For Venn Diagrams

Formulas For Venn Diagrams:-

Definitions:

Venn diagram, also known as Euler-Venn diagram is a simple representation of sets by diagrams.

  • Venn diagram representing mathematical or logical sets pictorially as circles or closed curves within a rectangle.
  • The usual picture makes use of a rectangle as the universal set and circles for the sets under consideration.

Basic Formula for the Venn Diagram

Some basic formulas for Venn diagrams of two and three elements.

n ( A ∪ B) = n(A ) + n ( B ) – n ( A∩ B)
n (A ∪ B ∪ C) = n(A ) + n ( B ) + n (C) – n ( A ∩ B) – n ( B ∩ C) – n ( C ∩ A) + n (A ∩ B ∩ C)

And so on, where n( A) = number of elements in set A.

After understanding the concept the of venn diagram with diagram, we don’t have to remember the formulas.

Venn Diagram in case of two elements.

formulas for venn diagram

Where; 
X = number of elements that belong to set A only
Y = number of elements that belong to set B only
Z = number of elements that belong to set A and B both (AB)
W = number of elements that belong to none of the sets A or B
From the above figure, it is clear that 
n(A) = x + z ; 
n (B) = y + z ; 
n(A ∩ B) = z;
n ( A ∪ B) = x +y+ z.
Total number of elements = x + y + z + w

Venn Diagram in case of three elements.


venn diagram formulas

 

Where,
W = number of elements that belong to none of the sets A, B or C

Read Also: Tips And Tricks to solve Venn diagram question

formulas for venn diagram