Formulas For Venn Diagrams

Concepts for Venn Diagram

When a collection of given sets is given. To find the all possible relations between sets , we draw Venn Diagram i.e. Venn Diagram is the representation to find the all logical relations between different sets. On this page we’ll look up for the Formulas For Venn Diagrams.

Definition and use of 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.
formulas-for-venn-diagram

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 for 2 sets

n ( A ∪ B) = n(A ) + n ( B ) – n ( A∩ B)
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 for 2 Sets

Venn Diagram for 3 sets

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

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

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