Definition:Venn Diagram

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

The following diagram illustrates the various operations between three sets.
 * VennDiagram.png

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 see

 * Definition:Euler Diagram