What is a Venn Diagram – Explain with Examples

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What is a Venn Diagram?

The term Venn diagram is not foreign since we all have had Mathematics, especially Probability and Algebra. Now, for a layman, the Venn diagram is a pictorial exhibition of all possible real relations between a collection of varying sets of items. It is made up of several overlapping circles or oval shapes, with each representing a single set or item.

Venn diagrams depict complex and theoretical relationships and ideas for a better and easier understanding. These diagrams are also professionally utilized to display complex mathematical concepts by professors, classification in science, and develop sales strategies in the business industry.

Venn diagram

Image Source: pinterest.com


Evolution of Venn Diagram

The growth of the Venn diagram dates back to 1880 when John Venn brought them to life in an article titled ‘On the Diagrammatic and Mechanical Representation of Propositions and Reasoning.’ It was in the Philosophical Magazine and Journal of Science. John Venn carried out a thorough research on these diagrams and foresaw their formalization. He is the one who originally generalized them, no wonder their naming, i.e., Venn Diagrams in 1918.

There is a small gap between Venn diagrams and Euler diagrams invented in the 18th century by Leonhard Euler, who also had a hand in its development in the 1700s. John used to refer to the charts as Eulerian circles.

The development of Venn diagrams continued in the 20thcentury. For instance, around 1963, D.W Henderson revealed the existence of an n-Venn graph consisting of n-fold rational symmetry, which pointed out that n was a prime number. This concept was delved into by four other intellects in the following years, who concluded that rotationally symmetric Venn diagrams only exist if n is a prime number.

Ever since, these diagrams have become part of today’s studying curriculum and illustrate business information. Venn and Euler’s diagrams got incorporated as a component of instruction in the set theory of the new math movement in the year 1960.


Why are Venn diagrams Important?

Venn diagrams are useful as a teaching and studying tools to scholars, teachers, and professors. They help represent simple mathematical concepts in grade schools as well as rocket-science kind of theories and problems among logicians and mathematicians.

Furthermore, together with Set theory, Venn diagrams have facilitated a clearer up-to-date understanding of infinite numbers and real numbers in Mathematics. They also enhanced the creation of a common language and system of symbols concerning Set theory among researchers and mathematicians.

They are ideal for illustrating similarities and differences among items or ideas when circles overlap or otherwise. This feature is commonly utilized in the business industry to find and create a niche in the market for goods and services. These facilitate incredible sales reports and huge realized profits among entrepreneurs.

You can also use Venn diagrams to make crucial life decisions, like what college to enroll in, what school to take your kid, the best material for construction or making a garment, which restaurant to dine in, etc.


When to Use Venn diagrams?

You can use Venn diagrams to demonstrate relationships is statistics, logic, probability, linguistics, computer science, business set up, and many more areas.

  • In Mathematics, Venn diagrams are a teaching tool that explains Math concepts like sets, unions, and intersections. They also solve severe problems in advanced mathematics. You can read extensively about them in academic journals in your library and be amazed at how Set theory is a complete mathematics branch.

    Statisticians employ the idea of Venn diagrams to foretell the chances of particular occurrences. It is also the case in the predictive analytics field. Sampled data sets are compared and scrutinized to point their similarities and differences.

statistical Venn diagram

Image Source: pinterest.com


  • They are also efficient in determining logical grounds in arguments and conclusions. Like in deductive reasoning in case the premises are real, and the argument form happens to be correct, the outcome thereof must be right. A similar diagram to the Venn one on logic is the Truth Table. It puts variables into columns to decipher what is logically possible. Another one is the Randolph diagram, aka R-Diagram, it uses lines to explain sets.

syllogism in a Venn diagram

Image Source: youtube.com


  • In linguistics, Venn diagrams help to learn about how languages differ or relate, in terms of the alphabet, vowels, pronunciation, etc.

Spanish vs. English Venn diagram

Image Source: slideshare.net


  • In computer science, geeks and programmers use Venn diagrams to get a clear picture of languages and hierarchies in computer systems.

data science Venn diagram

Image Source: kdnuggets.com


  • The diagrams are also useful in the sales and marketing field for comparing and contrasting products, services, processes, and all that goes on in business set-ups. They are practical and efficient in improving sales and profits and the broad running of enterprises.

business techniques Venn diagram

Image Source: businessbullet.co.uk


Venn Diagram Symbols

There are numerous symbols when it comes to a Venn diagram, but we are going to look at three. ꓵ - the intersection of two sets: shows the items that are common to both sets.

intersection in Venn diagram

Image Source: youtube.com

∪ - a complete Venn diagram represents this.

the union of sets in Venn diagram

Image Source: math-only-math.com


A’ – this denotes the completion of a set A. It consists of anything not included in the collection.

set complement in Venn diagram

Image Source: mathonline.wikidot.com


Venn Diagram Examples


The first Venn diagram example is in Mathematics. They are accessible when covering Sets Theory and Probability topics.

In the diagram below, there are two sets, A = {1, 5, 6, 7, 8, 9, 10, 12} and B = {2, 3, 4, 6, 7, 9, 11, 12, 13}. The section where the two sets overlap has the numbers contained in both Set A and B, referred to as the intersection of A and B. The two sets put together, gives their union which comprises of all the objects in A, B which are {1 2 3 4 5 6 7 8 9 10 11 12 13}.

math Venn diagram-set A and B

Image Source: bbc.co.uk



In the Venn diagram example below, it analyzes the commonalities and differences of different areas of work. Human Resource Managers and Career Experts use it to advise individuals in their career paths.

jobs Venn diagram

Image Source: pinterest.com



Scientist uses Venn diagrams to study human health and medicines. In the illustration below, you can see amino acids that are vital to human life.

amino acid Venn diagram

Image Source: researchgate.com


How to create a Basic Venn Diagram in Minutes?

Now, we will use EdrawMax’s online software. It has all the basic symbols and shapes you need alongside numerous Venn diagram free templates and a fancy and advanced interface that is easy on beginners.

Before starting the Venn diagram online, you have to ensure you:

  • Determine the goal you want to achieve. Have a clear understanding of what you would like to compare and for what purpose is the comparison needed. It facilitates the definition of sets.
  • Run through and come up with a list of items contained in the sets.
  • Peruse through the available templates to have a hint of what you are about to draw and then make your own Venn diagram using the following steps.


Step 1:  Log onto the software’s website from https://www.edrawmax.com/online/. If you had not created an account prior, sign in using valid credentials, verify your account then log in.

Step 2:  Select Business Diagram options from the Available Templates tab and double click on the Venn Diagram icon to display an empty page onto which you will draw.

Step 3:  On the left pane of the screen, you will find all the required Venn diagram symbols and shapes. Drag and drop appropriate ones and drop them onto the drawing canvas to make your Venn diagram.

Step 4:  Save the done Venn diagram in the available formats or export or share it to other platforms directly from the Edraw webpage.


Step 5:  Customization. Most in-built shapes are designed to allow for resizing, editing, and make color changes.


  • To resize a circle, drag the yellow icon on the edge of the circle and release it when you are satisfied with the new circle size.

  • To change the size of the intersection segment or reposition the circles, locate the yellow dot in the middle of the circle and drag it carefully until you achieve the desired adjustment.

  • To input, various circles, tap on the Actions button and choose Set Circle Number.

  • To input new text in a set, tap on the Textbox and type.

  • To make color changes, tap on the target circle, at a time more than once, and choose a color from the quick color tab at the bottom.

  • To incorporate a personal Theme and Style, choose from the available fonts, effects, and color schemes. Make a unique and professional Venn diagram by clicking on what you prefer.



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