10 what are the various parts of the venn diagram Ideas

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Venn Diagram? Components, Examples, and Applications

What Is a Venn Diagram?

A Venn diagram is an illustration that uses circles to show the relationships among things or finite groups of things. Circles that overlap have a commonality while circles that do not overlap do not share those traits.

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Venn diagrams help to visually represent the similarities and differences between two concepts. They have long been recognized for their usefulness as educational tools. Since the mid-20th century, Venn diagrams have been used as part of the introductory logic curriculum and in elementary-level educational plans around the world.

Understanding Venn Diagrams

Venn diagrams are useful for illustrating how different concepts or factors intersect with one another. They can show, at a glance, how things are similar or different and where and how they overlap. Often, the center of a Venn diagram (the intersection of two or more circles) represents some nexus or main idea that can be decomposed into the various other circles, with labels on the outer portions more general and distinct ideas than those toward the center.

The overlapping areas can also be used to show where two otherwise disparate contexts share commonalities. For instance, in the example diagram below we see that while the urban and rural contexts are distinct with their own set of acivities, they also do share sporting events.


Venn Diagram (click to enlarge).
Grace Fleming

Venn Diagram Components

While there are many ways to organize a Venn diagram, they most often consist of overlapping circles. Each circle by itself represents a set, which may include ideas, concepts, numbers, or objects.

When circles overlap or intersect, those sub-sets that are shared are known as a union or intersection. Areas that don’t overlap show differences between sets, and a complement set refers to everything not shared by a particular set or sub-set.

The History and Origin of Venn Diagrams

The English logician John Venn popularized the diagram in the 1880s. He called them Eulerian circles after the Swiss mathematician Leonard Euler, who created similar diagrams in the 1700s.

The term Venn diagram did not appear until 1918 when Clarence Lewis, an American academic philosopher and the eventual founder of conceptual pragmatism, referred to the circular depiction as the Venn diagram in his book A Survey of Symbolic Logic.

Venn studied and taught logic and probability theory at Cambridge University, where he developed his method of using diagrams to illustrate the branch of mathematics known as set theory. He published a precedent-setting work, The Logic of Chance, which explained the frequency theory of probability. In it, he argued that probability, contrary to popular assumption, should be established based on the regularity with which something is predicted to occur. In another book, Symbolic Logic, Venn built on and developed mathematician George Boole’s theories on algebra. This work helped him develop the Venn diagram.

Venn diagrams have been used since the mid-20th century in classrooms from the elementary school level to introductory logic.

Applications for Venn Diagrams

Venn diagrams are used to depict how items relate to each other against an overall backdrop, universe, data set, or environment. A Venn diagram could be used, for example, to compare two companies within the same industry by illustrating the products both companies offer (where circles overlap) and the products that are exclusive to each company (outer circles). 

Venn diagrams are, at a basic level, simple pictorial representations of the relationship that exists between two sets of things. However, they can be much more complex. Still, 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, and business.

Examples of Venn Diagrams

A Venn diagram could be drawn to illustrate fruits that come in red or orange colors. Below, we can see that there are orange fruits (circle B) such as persimmons and tangerines while apples and cherries (circle A) come in red colors. Peppers and tomatoes come in both red and orange colors, as represented by the overlapping area of the two circles.

Image by Julie Bang © Investopedia 2020

You might also draw a Venn diagram to help decide which of two cars to purchase. The Venn diagram shows the features that are exclusive to each car and the features that both cars have.

Below, we see that Car A is a sedan that’s powered by gasoline and gets 20 miles per gallon, while Car B is a hybrid, gets 40 miles-per-gallon for mileage, and is a hatchback.

Image by Julie Bang © Investopedia 2020

The shaded region where the two circles overlap shows the features that both cars have in common, which include a radio, four doors, Bluetooth capability, and airbags.

The Venn diagram graphically conveys the similarities and differences between the two cars to help decide which to purchase.

What Is a Venn Diagram in Math?

A Venn diagram in math is used in logic theory and set theory to show various sets or data and their relationship with each other.

How Do You Read a Venn Diagram?

A Venn diagram is read by observing all of the circles that make up the entire diagram. Each circle is its own item or data set. The portions of the circles that overlap indicate the areas that are in common amongst the different items whereas the parts that do not overlap indicate unique traits among the item or data set represented by the circle.

Why Are They Called Venn Diagrams?

They are called Venn diagrams because the diagram was developed by John Venn, an English logician.

What Is the Middle of a Venn Diagram Called?

The middle of a Venn diagram where two or more sets overlap is known as the intersection.

Does a Venn Diagram Always Use 2 or 3 Circles?

While often employing a pair or triplet of circles, Venn diagram can use any number of circles (or any other shape) to show the differences and intersections of different sets.

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What Is a Venn Diagram? Components, Examples, and …

What Is a Venn Diagram? Components, Examples, and ...

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  • Sumary: A Venn diagram is an illustration that uses circles to show the commonalities and differences between things or groups of things.

  • Matching Result: A complete Venn diagram represents the union of two sets. ∩: Intersection of two sets. The intersection shows what items are shared between categories.

  • Intro: What Is a Venn Diagram? Components, Examples, and Applications What Is a Venn Diagram? A Venn diagram is an illustration that uses circles to show the relationships among things or finite groups of things. Circles that overlap have a commonality while circles that do not overlap do not share those…
  • Source: https://www.investopedia.com/terms/v/venn-diagram.asp

Frequently Asked Questions About what are the various parts of the venn diagram

If you have questions that need to be answered about the topic what are the various parts of the venn diagram, then this section may help you solve it.

What three components make up a Venn diagram?

The intersections, sets, and unions make up a Venn diagram.

What is the name of the basic Venn diagram component?

The intersection is the location in the center of a Venn diagram where two or more sets cross over.

What is a four-venn diagram?

The four circles in the diagram represent the four different groups, and the overlapping area between the circles represents the ways that they are related. A four circle venn diagram template is a visual tool that can be used to help show how four different groups or concepts are related.

What is a four-way Venn diagram?

Draw three circles that partially or completely intersect each other first, then add another circle to the outside of this arrangement, label the regions with the names of each set, and shade in those regions where two different sets overlap to create a four-way Venn diagram.

Can there be 4 sets in a Venn diagram?

The intersections of four or more sets cannot all be represented by circles in a Venn diagram, which is impossible to do.

In a Venn diagram, how many sections are there?

Venn diagrams typically depict two or three sets, though some versions support more.

What exactly does in Venn diagrams mean?

: The intersection of two sets. The intersection reveals the items that are common to both categories.

What does a B mean?

The intersection of the two committees in the preceding example is represented by the set consisting of Blanshard and Hixon. The set A? B, also known as the “A intersection B” or “the intersection of A and B,” is defined as the set composed of all elements that belong to both A and B.

What exactly does in Venn diagrams mean?

2.2 The intersection of two sets is denoted by the Venn diagram symbol?. In the Venn diagram, the intersection is the region where the two circles overlap. An intersection set has all the members that are shared by both sets or categories.

What is an AC?

The common element of the two sets is given by A intersection B intersection C, which is typically written as A n B n C. The intersection symbol ‘n’ stands for intersection and indicates the common element of the two sets.

What does mean in math?

According to the definition given above, the intersection of two sets A and B is the collection of all the elements that are shared by both A and B. Symbolically, the intersection of A and B is denoted by the symbol “?.”

What exactly does A B C mean?

A?(B?C)?(A?B)?(A?C) If you have an element either from set A or from both sets B and C, then you have elements which are from both either sets A or B and from either sets A or C.? means intersection: B?C is set of elements in both set B and set C.? means union: A?B is set of elements in either set A or set B.

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