We explain what a Venn diagram is, what it is for and its elements. In addition, we tell you what types exist and how to make them.

## What is a Venn diagram?

The Venn diagram is a type of graphic organizer that shows how two or more sets of elements are related, since, **Using overlapping circles, represents which characteristics they share and which they do not. ** two or more categories, groups, ideas, concepts, theories, among others.

In the Venn diagram there are:

**a rectangle**. It represents the universe, that is, the totality of elements, and is designated with a title. In some diagrams there is no rectangle, but there is a title.**Two or more circles**. They represent sets, ideas, concepts or categories that are designated with a title or a sentence.**Words or phrases**. They represent the elements of a set, the members of a category or a series of characteristics.**An overlap between the circles**. It represents the links between sets, which can be intersection, inclusion or disjunction.

For example, in a diagram about mammals, the universe is *characteristics of mammals* and there are two sets:* land mammals* and *aquatic mammals*. In each circle, the characteristics shared by the members of each class are written and in the superposition of both circles, the common characteristics of both sets are noted.

## Features of the Venn diagram

Unlike most graphic organizers, the Venn diagram allows you to:

- Identify what and how many sets there are in relation to a topic.
- Show what link there is between the sets.
- Indicate which set each element belongs to and, in some cases, identify elements that are part of two or more sets.
- Determine that there may be elements that do not belong to any set.

## What is the Venn diagram for?

The Venn diagram has great advantages and is used for different purposes:

**Display information visually**. Helps organize information so it is easier to understand.**Allows you to graph the relationship between two or more sets**. It is used to see what characteristics or what elements two or more sets have in common and what their differences are.**It is useful for making classifications**. It is used to determine which elements belong to each category.**Allows comparisons**. It serves to contrast the characteristics or elements of objects, products, places, theories, among others.**It is a tool for making decisions**. It allows you to see two or more options more clearly and reflect on which is the most convenient.

## Types of Venn diagram

There are different types of Venn diagrams, depending on the type of relationship established between the sets:

### Intersection Venn Diagram

It shows that there are elements that belong to one set or the other and elements that belong to both. There may be two or more circles, depending on how many sets there are. For example:

The element *frog* It is at the intersection, because it is an animal that lives both on land and in water.

### Inclusion Venn Diagram

Shows that a set includes a subset. For example:

Set B (*living beings*) includes subset A (*mammals*), and, since there are no mammals that are not living beings, the part of the circle is shaded or crossed out *mammals* which is not included in *living beings*. In addition, the graph indicates that there are other living beings that are not mammals, such as the snake, the iguana and the condor.

### Disjunction Venn Diagram

Shows that sets contain elements that do not belong to other sets. For example:

The overlapping circles are shaded or crossed out, to represent that no element of the set *reptiles* can belong to the set *birds *and vice versa.

## How to make a Venn diagram?

To make a Venn diagram, you can follow a series of steps:

**Determine the topic**. You must select the topic and what aspects you want to compare. For example, you can compare the characteristics of two cars.**Write down all the items in a list**. You can brainstorm to write down all the elements or characteristics. For example, you can write all the most important characteristics of cars in general.**Determine the sets**. You must determine which sets the elements or characteristics will go in and draw a circle for each set. If two cars are compared, there will be two overlapping circles, one for car A and one for car B.**Indicate which element belongs to each set**. The elements or characteristics must be noted in their corresponding set. If any element or characteristic belongs to two sets, it is written in the sector where the circles overlap. For example, the “fast” feature is only present in car A, so it will be noted in the first circle; The “comfortable” characteristic is only present in car B, so it will be written in the second circle; and the “economy” feature is found on both cars, then it will be noted on the overlay.

## Venn diagram examples

In this diagram, there are two sets: *numbers multiples of two *and *numbers multiples of three. *In each circle, the corresponding numbers are noted, and in the superposition, those that are multiples of two and three, that is, that belong to both sets.

In this diagram, the point of customer satisfaction that is achieved when there is a balance between customer expectations, product quality, and product price is measured.

In this diagram, there are three sets: *animals that move on land, animals that move through water *and *animals that move through the air. *In each circle, the animals that belong to one class are noted, and at the intersections, those that belong to two or more sets.

In this diagram, the characteristics of the sets are mentioned *bushes, trees* and *ferns*. At the intersections, the characteristics that two or more types of plants have in common are noted. However, the overlaps of *shrubbery* and *ferns* and of *trees *and *ferns *They are crossed out, because they have no characteristics in common.

## Areas in which the Venn diagram is used

The Venn diagram is used for different purposes depending on the discipline:

**Math**. It serves to teach and learn numerical sets and their links in a didactic way. It is also applied in solving equations and problems and in probabilistic analysis.**Statistics**. It is used to compare data when analyzing how a variable manifests itself in a population.**Logic**. It serves to represent propositions and analyze the validity of arguments.**Teaching**. It is used to classify different elements and to compare theories, concepts and characteristics in various subjects, such as language, literature, social sciences and natural sciences.**Business area**. It is used to analyze and compare products, services, customer needs, production processes, projects, among others.**Computing**. It is used to analyze and compare different types of data, such as algorithms and user preferences and searches.

## Venn Diagram Glossary

Venn diagrams are used to graphically represent sets and their operations in set theory. In this theory, specific terms are used, some of the most important are:

**Universe**. It is that which contains all the elements. For example, a universe can be made up of all numbers that are multiples of others.**Set**. It is something that contains a group of elements that share one or more characteristics. For example, in a diagram there are two sets:*numbers that are multiples of 3*and*numbers that are multiples of 4*.**empty set**. It is a set that does not contain any elements. For example, if the universe is*all the books in a library*and there are no geography books, it is argued that*geography books*It is an empty set.**Element**. He is a member of a group. For example, 3, 6 and 9 are elements of the set*multiples of 3*.**Inclusion**. It is the link that indicates that a set includes a subset. For example, the set*multiples of 9*is included in the set*multiples of 3*.**Belonging**. It is the link between an element and its set, that is, it shows that an element belongs to a set. For example, the number 6 belongs to the set*multiples of 3*.**Non-belonging**. It is the link that indicates that an element does not belong to a set. For example, the number 8 does not belong to the set*multiples of 3*.**Union**. It is the formation of a new set that occurs when all the elements of one set belong to that of another and vice versa. For example, the sets*philosophy books*and*literature books*come together to form the whole*humanities books*.**Intersection**. It is the group of elements that have characteristics of two or more different sets. For example, the numbers 12, 24, 36 are at the intersection, because they belong to the sets*multiples of 3*and*multiples of 4*.**Difference**. It is the group of elements that are part of one set, but not another. For example, the numbers 3, 6 and 9 belong to the set*multiples of 3*but not to the whole*multiples of 4*.**Complement**. It is the group of elements that do not belong to a set. For example, the numbers 1, 2, and 4 are not part of the set*multiples of 3*.

## History of the Venn diagram

The Venn diagram emerged in 1881, with the publication of *Symbolic Logic*by John Venn, a British mathematician and logician. In that book, the author developed the different types of graphs that are known today, but applied to the representation of propositions that were used in algebra.

The graphs invented by Venn have several antecedents, but the most notable were those designed by Leonhard Euler, a Swiss physicist and mathematician. Venn simplified the Euler schemes, since he proposed a single diagram that with small modifications could represent all the propositions.

The main differences between the Venn diagram and the Euler diagram are:

- The Euler diagram that represents inclusion or the proposition “All A is B” consists of drawing the circle of the set A inside the circle of the set B. On the other hand, in the Venn diagram, two overlapping circles are drawn and the circle is crossed out. part of set A that is not included in set B.

- The Euler diagram representing the disjunction or the proposition “No A is B” consists of two separate circles. On the other hand, in the Venn diagram, the overlapping of the circles is crossed out, so that it is nullified.

#### References

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*Cognotechniques: Tools to think more and better*. Alfaomega.