How Venn Diagrams Revolutionised Visualisation in Mathematics?

Venn Diagrams are used extensively across the whole world to understand and visualize mathematical set operations in a logical way. It was popularized by John Venn in the 1880s and thus, is named after him. In this article, we will discuss the importance of the Venn diagram and know the history of its origin. We will also learn about a few Venn diagram nomenclature.

What is a Venn Diagram?

A Venn diagram is a diagram that uses superimposed circles or other shapes to illustrate the logical relationship between two or more sets of operations. You can use these diagrams to graphically organize things and find out how various items are similar and at the same time different from one another.

You must have noticed that these diagrams are easily understandable. Solving a problem related with Venn diagrams won’t feel like any problem to you if you have conceptual clarity of this topic and here is where Cuemath’s role comes into play. It has a presence in more than twenty countries. Cuemath is the best online math services platform which helps you in building excellent mathematical foundations. Visit Cuemath website, if you want to learn about these concepts in detail and in an interactive way.

Importance of Venn Diagrams

  • Helps in solving complex mathematical problems: Tedious problems that require usage of mathematical formulae can be solved easily with the help of Venn diagrams.
  • Helps in comparing data sets: Venn diagrams are used extensively to compare data sets and find out probabilities.
  • Helps in visually arranging information: Information of two or more sets of operations can be arranged using Venn diagrams which helps its user to find out the differences and commonalities between the set of operations. Students can also use it to think through the logic behind a concept which can range from basic level problems to advanced levels.
  • Uses of mathematics in various other subjects: Subjects like Statistics, Business Studies, Linguistics, Computer Science and so on takes help of Venn diagrams extensively.

Venn Diagram Nomenclature

  • Set: A set is a well-defined collection of various objects.
  • Union of Sets: All the items in the sets together are called union.
  • Intersection of Sets: Let there be two sets P and Q. The intersection of set P and set Q is the set of all elements which are common to both P and Q.
  • Difference of Sets: The difference of the sets A and B in this order is the set of elements which belong to A but not to B. We write A-B to denote it symbolically.
  • Universal Set: It is the set of all the elements present in the related sets.
  • Complement Set: It is the set that includes all the elements of the universal set which are not present in the given set.

History of Origin of Venn Diagrams

The credit of popularising Venn diagrams goes to the English logician, John Venn after which this concept is named. The use of diagrams to illustrate mathematical and logical operations had existed prior to John Venn’s work. Venn himself avoided the term “Venn diagram” and referred to his work as “Eulerian Circles”. The diagrams introduced by Venn are very similar to Euler diagrams, which were invented by Leonhard in the 18th century. Works of mathematics similar to the Venn diagram have also been found in the works of a few early Aristotelian scholars. In 1686, the genius polymath, Gottfried Wilhelm Leibniz illustrated all valid syllogisms of Aristotle through circle drawings. However, much of this work remained unpublished.

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As part of the New Math movement in the 1960s, Venn diagrams as well as Euler’s diagrams were included as part of the instruction in set theory. Developments took place in the twentieth century, and they continue to develop even today. Visit Cuemath website and get hold of these topics by interacting with top teachers around the world.