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.

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

• Euler diagram

Source of Name

This entry was named for John Venn.

Sources

• W.E. Deskins: Abstract Algebra (1964): $\S 1.1$
• Seth Warner: Modern Algebra (1965)... (previous)... (next): $\S 3$
• Richard A. Dean: Elements of Abstract Algebra (1966): $\S 0.2$
• B. Hartley and T.O. Hawkes: Rings, Modules and Linear Algebra (1970): $\S 1.2$: Ring Example $6$
• Thomas A. Whitelaw: An Introduction to Abstract Algebra (1978)... (previous)... (next): $\S 6$