# Definition:Venn Diagram

## Definition

A Venn diagram is a technique for the graphic depiction of the interrelationship between a small number (usually $3$ or fewer) of sets.

The following diagram illustrates the various operations between three sets.

The circles represent the sets $S_1$, $S_2$ and $S_3$.

The white surrounding box represents the universal set $\mathbb U$.

Each of the areas inside the various circle represents an intersection between the various sets and their complements, as follows:

The gray area represents $S_1 \cap S_2 \cap S_3$.
The purple area represents $S_1 \cap S_2 \cap \overline {S_3}$.
The orange area represents $S_1 \cap \overline {S_2} \cap S_3$.
The green area represents $\overline {S_1} \cap S_2 \cap S_3$.
The red area represents $S_1 \cap \overline {S_2} \cap \overline {S_3}$.
The blue area represents $\overline {S_1} \cap S_2 \cap \overline {S_3}$.
The yellow area represents $\overline {S_1} \cap \overline {S_2} \cap S_3$.
The surrounding white area represents $\overline {S_1} \cap \overline {S_2} \cap \overline {S_3}$.

The notation $\overline {S_1}$ denotes set complement.

If it is required to show on a diagram that a particular intersection is empty, then it is generally shaded black.

## Also known as

Some sources spell this without the uppercase V: venn diagram.

## Also see

• Results about Venn diagrams can be found here.

## Source of Name

This entry was named for John Venn.