Venn diagrams are commonly used in mathematics, statistics, logic, education, linguistics, computer science, and business. They are also known as Set diagrams or Logic diagrams. Since the Venn diagram became part of “new math” curricula in the 1960s, many people first encountered them in school while studying math or logic. These can range from simple diagrams with two or three sets of a few elements to quite sophisticated diagrams with six or seven sets and beyond, including 3D presentations.
They are used to consider and depict how items relate to one another within a specific “universe” or segment. Venn diagrams are commonly used in presentations and reports because they allow users to visualise data in clear and powerful ways. They are related to Euler diagrams, which differ in that they omit sets if no items exist in them. Even if a set is empty, Venn diagrams show relationships.
History of Venn Diagrams
Venn diagrams are named after John Venn, a British logician. He discussed them in a paper published in the Philosophical Magazine and Journal of Science in 1880 titled “On the Diagrammatic and Mechanical Representation of Propositions and Reasonings.” However, the origins of this type of diagram can be traced back at least 600 years. In a 1969 article tracing their history, Baron wrote about them. She also attributed similar diagrams to Gottfried Wilhelm von Leibnitz, a German mathematician, and philosopher who lived in the late 1600s.
Of course, Venn diagrams can get much more complicated than that, as they are widely used in a variety of fields.
Over the last 60 years, experts David W. Henderson, Peter Hamburger, Jerrold Griggs, Charles E. “Chip” Killian, and Carla D. Savage have made significant contributions to the evolution of Venn Diagrams. Their research focused on symmetric Venn Diagrams and their relationship to prime numbers, which are numbers that are not divisible by any other number except 1 and the number itself. Victoria, a symmetric diagram based on the prime number 7, is well-known in math circles.
Examples of Venn Diagram
Assume our universe is about pets, and we want to see which type of pet our family would prefer.
- Set A includes my favourite animals: a dog, a bird, and a hamster.
- Set B includes Family Member B’s favourite pets: a dog, a cat, and a fish.
- Set C contains the preferences of Family Member C: dog, cat, turtle, and snake.
- Only dog appears in the overlap, or intersection, of the three sets. It appears that we will be getting a dog.
- Of course, Venn diagrams can get much more complicated than that, as they are widely used in a variety of fields.
Purpose of Venn Diagrams
- To visually organise information so that the relationship between groups of items, such as similarities and differences, can be seen. Students and professionals can use them to think through the logic behind a concept as well as to depict the relationships for visual communication. This objective can range from basic to advanced. To contrast two or more options and clearly see what they have in common versus what might set them apart. This could be done when deciding on a critical product or service to purchase.
- To solve difficult mathematical problems. Of course, this is assuming you’re a mathematician.
- To compare data sets, find correlations, and predict the likelihood of certain events.
- To deduce the logic behind statements or equations, such as the Boolean logic behind a word search involving “or” and “and” statements and how they are grouped.
You’ve probably noticed that these diagrams are simple to understand. Solving a problem involving Venn diagrams will not feel like a problem if you have conceptual clarity on the subject, and this is where Cuemath comes into play.
Go to the Cuemath website. It is present in over twenty countries. Cuemath is the best online math services platform for laying strong mathematical foundations. If you want to learn about these concepts in-depth and in an interactive way, go to the Cuemath website.