What is a Venn Diagram?
Definition
A Venn diagram shows all possible membership combinations of the sets being compared. For two or three sets, overlapping circles are a familiar layout. A region can be empty; its presence does not mean the sets actually share an element. Euler diagrams instead draw the relationships that apply to the particular sets. See the Stanford Encyclopedia of Philosophy discussion of set diagrams.
To draw the sets and label their overlaps, use the online Venn diagram tool and keep each region tied to the relationship it represents.
History and Origin
The Venn diagram was introduced and popularized in the 1880s by John Venn, a British logician and philosopher. John Venn studied mathematics and logic at Cambridge University and later became a lecturer and fellow at the university. During his time at Cambridge, he developed his groundbreaking ideas on the diagrammatic representation of sets.
In 1880, John Venn published a paper entitled “On the Diagrammatic and Mechanical Representation of Propositions and Reasonings,” which presented his diagrammatic method for representing sets and logical relationships. This article introduced what we now know as Venn diagrams. Since then, Venn Diagram has gained significant recognition and acceptance, and has quickly been applied to various fields.
Formula
Here’s a basic formula for Venn Diagram of two sets:
n ( A ∪ B) = n(A ) + n ( B ) – n ( A∩ B)
For the regions labeled in Figure 1:
X = number of elements in A only, excluding the overlap.
Y = number of elements in B only, excluding the overlap.
Z = number of elements in both A and B, the intersection A ∩ B.
Figure 1
Count each region once:
n(A) = X + Z;
n(B) = Y + Z;
n(A ∩ B) = Z;
n(A ∪ B) = X + Y + Z.
Worked example: if 12 students choose only music, 8 choose only sport and 5 choose both, then n(A) = 17, n(B) = 13 and n(A ∪ B) = 25. Adding 17 + 13 counts the five students in both groups twice, so subtract 5.
Symbols
Set
A set is a collection of distinct elements. In a diagram, a closed boundary represents membership in that set.
Union (A∪B)
All elements in A, in B, or in both, counted once.
Intersection (A∩B)
The overlapping section, representing all elements shared or common within the selected sets.
Symmetric difference
Elements in A or B but not both: the two regions outside the overlap.
Relative complement
For example, A \ B contains the elements in A that are not in B.
Absolute complement (Ac)
The complement of A is everything in the specified universal set U that is not in A. The surrounding rectangle can represent U; elements outside U are outside the scope of the diagram.
Why use a Venn Diagram?
Visual organization: Venn diagrams allow information to be presented in a structured and organized manner. Hence, they help to visually organize information to see the logic behind the relationships of particular elements.
Logical Analysis: Venn diagrams help to reason complex issues through logic. They make it easier to identify logical implications, inconsistencies, or contradictions. In this way, complex mathematical problems can be reduced to a clear and understandable format.
Data comparison: use a Venn diagram to show shared and unique items in a few sets. Counts can support probability calculations when the population and sampling assumptions are defined; overlap alone does not establish correlation or predict an outcome.
Decision-making: By leveraging the visual power of Venn diagrams, decision-makers can gain a clearer understanding of the options, criteria, trade-offs, and commonalities involved in their decision-making processes. This can lead to more informed and effective decision-making outcomes.
Venn Diagrams in Real Use
Venn diagrams have brought great convenience to people in diverse fields. The streamlined purpose of the Venn diagram to illustrate concepts and groups has led to their popularized use in many fields, including statistics, linguistics, logic, education, computer science, business, etc.
In Education
The Venn diagram was initially regarded as a pedagogical tool and is still widely used in the classroom. Originally used to show the differences and similarities between scientific or logical concepts, it has expanded to other subjects. It can be used for comparing and contrasting, understanding set theory, visualizing data, and is also helpful in categorization and classification, literature analysis, vocabulary development, and so on.
For example, Venn diagrams are commonly employed to teach set theory concepts. Students can use the diagrams to represent sets, elements, intersections, and unions. This helps them grasp the fundamental principles of set theory, such as subsets, complements, and set operations. As for vocabulary development, Venn diagrams help expand students’ vocabulary. They can be used to illustrate word relationships, such as synonyms, antonyms, or word families. Students can better understand word meanings and usage by comparing and contrasting related words.
In Academia
In research, a Venn diagram can summarize overlap between a small number of lists, such as the items found by two search methods. Label the source and selection rule for each set.
In the research field, understanding the relationships between different datasets is vitally important for data analysis, and the use of suitable visualization methods is especially important for clarifying established relationships. Hence, generating a Venn diagram is one of the simplest and most effective ways to illustrate these relationships.
Venn diagrams are widely used in biological research, especially in genetic studies. For example, a Venn diagram is one of the most effective ways of examining the overlap of resulting gene lists. Accordingly, various Venn diagram application tools are freely available for particular research needs, such as Venny, VennPlex, and VENNTURE.
In Business
Business is a field where Venn diagrams can be extremely useful because there are always things to compare and consider when making decisions in different corporate settings. For example, these diagrams are often applied for market analysis, competitor analysis, product comparison, project management, risk management, etc.
For market segmentation, define the groups first—for example, customers who bought product A and customers who bought product B within the same period. The intersection then has a clear meaning. A Venn diagram does not show task order or calculate a project’s critical path.
Here’s a Venn diagram example applied in the business field concerning customer satisfaction and enterprise longevity.
The illustration below uses three overlapping themes to discuss customer satisfaction. It is a conceptual model, not measured evidence that those factors guarantee business longevity.
Figure 2
The central overlap combines customer requirements, product quality and price. Use the model to ask which factors matter to your customers, then gather evidence for those assumptions.
How to make a Venn diagram in Boardmix?
Boardmix is a powerful online collaborative whiteboard that integrates various tools to boost team efficiency and free team imagination. It offers a user-friendly interface that allows users to create, edit, and collaborate on a variety of digital boards. On this virtual whiteboard, you can easily brainstorm ideas, visualize concepts, and share your thoughts.
Versatility is one of the standout features of Boardmix. You can easily add text, images, drawings, sticky notes, and multimedia elements to your boards. It integrates various shapes, text boxes, and a range of expressive drawing tools, allowing you to easily create and edit Venn diagrams.
Use Boardmix to make a Venn diagram
1) Access Boardmix & Create a new board: Visit the Boardmix website (or open the Boardmix application) and sign in to your account. (If you don’t have an account, you can create one for free.) Once logged in, create a new board by selecting the option to start a new project or board.
2) Choose the Venn diagram template or make one yourself: Look for a Venn diagram template among the options Boardmix provides in the template gallery. You can also create one using different shapes.
3) Customize your Venn diagram: If you select the Venn diagram template, you’ll be taken to the canvas, where you can customize and edit the diagram. You can modify the size and layout of the circles or ellipses.
4) Add labels & populate the sets: Use the text tool or text boxes to add labels or titles to each set and the overlapping regions if needed. Depending on the purpose of your Venn diagram, populate each set by adding elements or items. You can use shapes, text boxes, sticky notes, or images to represent the elements within each set.
5) Customize further: Boardmix offers various customization options, including colors, fonts, line styles, and shapes. You can modify these elements to make your Venn diagram visually appealing and easy to understand.
6) Collaborate and share: If you’re working with a team or want to gather feedback, you can invite collaborators to join your board. Boardmix allows real-time collaboration, where multiple users can edit the Venn diagram simultaneously. You can also share the board with others by generating a shareable link or exporting the diagram in a compatible format.
