Venn Diagram

A Venn diagram uses overlapping circles or other shapes to illustrate the logical relationships between two or more sets of items. They are commonly used to graphically organize or compare items, involving two or three sets of a few elements, or 3D presentations, as they progress to six or seven sets and beyond. Also called Set diagrams or Logic diagrams, Venn Diagrams are widely used in mathematics, statistics, linguistics,  logic, teaching, computer science, and business.

Quick details

What: Discover Interconnections, Proportion

Why: Explore logical interrelationships through visual simplicity

History of Venn Diagram

Named after British logician John Venn, these charts were mentioned in the ‘1880 paper entitled “On the Diagrammatic and Mechanical Representation of Propositions and Reasonings” in the Philosophical Magazine and Journal of Science. But the roots of this type of diagram go back much further, at least 600 years. In the 1200s, philosopher and logician Ramon Llull of Majorca used a similar type of a diagram. A German mathematician and philosopher Gottfried Wilhelm von Leibnitz is credited to have drawn similar diagrams in the late 1600s. Venn diagrams are very similar to Euler diagrams, which were invented by Leonhard Euler in the 18th century.

Venn diagram showing the uppercase glyphs shared by the Greek, Latin, and Russian Cyrillic alphabets



When to Use a Venn Diagram?

1To visualize the relationship between sets of items, such as commonalities and differences

Use Venn diagrams to visually organize information,  to compare and contrast products, services, processes or anything that can depicted in sets. Venn Diagrams are an effective communication tool to illustrate comparison. Through both elementary or advanced Venn diagrams, logical relationships could be visualized to represent intersections, unions, symmetric differences, relative and absolute complements of sets.

Representation of various operations on Venn Diagrams


2To compare two or more choices and predict probabilities

Use Venn diagrams to predict the likelihood of certain occurrences. In statistics, Venn diagrams can be used to compare different sets of data and find degrees of commonality and differences. These correlations can help in the prediction of probabilities of certain occurrences. This aspect helps in predictive analysis of datasets. Venn diagrams have been used also used to study the commonalities and differences among languages.

An area proportional Venn Diagram where each shape is proportional to the number of elements it contains

3To reason through the logic

Venn diagrams are commonly used to determine the validity of particular arguments and conclusions. In deductive reasoning, if the premises are true and the argument form is correct, then the conclusion must be true. To reason through the logic behind statements or equations, such as the Boolean logic behind a word search involving “or” and “and” statements and can be visually represented through Venn diagrams. Venn diagrams also correspond to truth tables for the propositions x in A, x in B, etc. in the sense that each region of Venn diagram corresponds to one row of the truth table.

Venn’s four-set diagram using ellipses of the pan-genome of the genus Acholeplasma

Types of Venn Diagram

1. Scaled Venn Diagram

This is also called as the area proportional diagram where the circles (or other shapes) are sized by their proportional representation of the whole.

2. Randolph diagram

R-diagram is a simple way to visualize logical expressions and combinations of sets, using intersecting lines.

3. Euler Diagram

This is a diagrammatic means of representing sets and their relationships, particularly useful for explaining complex hierarchies and overlapping definitions. However, unlike Venn diagrams, which show all possible relations between different sets, the Euler diagram shows only relevant relationships.


When Not to Use a Venn Diagram?

1When there are many classes of objects to represent, Venn, becomes complex to understand

Do not use Venn diagrams when reasoning about many classes of objects, as it becomes complicated to understand the information. Venn diagrams work well with at most three circles and going beyond that, making mistakes while encoding information can happen. It is possible to add more bounded regions if we are dealing with more than three classes, but then the resulting diagrams become rather difficult to handle and interpret.

2When a clear comprehension is needed

Venn diagrams are limited in their nature as they have limited expressive power in accurately representing pieces of information that cannot be accurately represented. For example, the system of notation allows us to talk about classes of objects, but not particular individual objects.  We might have to introduce new symbols, using dots to represent individuals objects.


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