Definition:Venn Diagram
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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.
Sources
- 1964: W.E. Deskins: Abstract Algebra ... (previous) ... (next): $\S 1.1$
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text I$: Algebraic Structures: $\S 3$: Unions and Intersections of Sets
- 1966: Richard A. Dean: Elements of Abstract Algebra ... (previous) ... (next): $\S 0.2$. Sets
- 1970: B. Hartley and T.O. Hawkes: Rings, Modules and Linear Algebra ... (previous) ... (next): Chapter $1$: Rings - Definitions and Examples: $2$: Some examples of rings: Ring Example $6$
- 1972: A.G. Howson: A Handbook of Terms used in Algebra and Analysis ... (previous) ... (next): $\S 2$: Sets and Functions: Sets
- 1975: T.S. Blyth: Set Theory and Abstract Algebra ... (previous) ... (next): $\S 1$. Sets; inclusion; intersection; union; complementation; number systems
- 1975: Bert Mendelson: Introduction to Topology (3rd ed.) ... (previous) ... (next): Chapter $1$: Theory of Sets: $\S 3$: Set Operations: Union, Intersection and Complement
- 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 6$: Subsets
- 1986: Geoffrey Grimmett and Dominic Welsh: Probability: An Introduction ... (previous) ... (next): $1$: Events and probabilities: $1.4$: Probability spaces
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Venn diagram
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Venn diagram
- 2012: M. Ben-Ari: Mathematical Logic for Computer Science (3rd ed.) ... (previous) ... (next): Appendix $\text{A}.2$
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Venn diagram