# Formulas For Venn Diagrams

## Formulas 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. ### 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 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 formula 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