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.