Venn Diagram

Venn Diagram

A Venn diagram is a technique for the graphic depiction of the interrelationship between a small number (usually 3 or less) of Sets. Venn diagrams were introduced in 1880 by John Venn.

Usually we knew about Venn Diagrams of 2 to 3 variable, lets us take a leap and learn more about Venn Diagram of 4 variables.

The Venn diagram consists of four sets, A, B, C, and D. the total possible subsets are 16.

Each of the sixteen regions represents the intersection over a subset of {A, B, C, and D}. The tree diagram below displays the sixteen possible subsets. We can assign different numbers to different possible set for more clarity as shown below

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Each of the areas inside the various shapes represents an intersection between the various sets and their complements, as follows:

                                  

• The area 1 represents A∩B∩C∩D.
• The area 2 represents A∩B∩C.
• The area 3 represents A∩B∩D.
• The area 4 represents A∩B.
• The area 5 represents A∩C∩D.
• The area 6 represents A∩C.
• The area 7 represents A∩D.
• The area 8 represents A.
• The area 9 represents B∩C∩D.
• The area 10 represents B∩C.
• The area 11 represents B∩D.
• The area 12 represents B.
• The area 13 represents C∩D.
• The area 14 represents C.
• The area 15 represents D.
• The area 16 represents Universal Set.

Another shape which can be used for depicting 4 sets is eclipse called as Venn's four-set diagram

Edwards' Venn diagrams

A.W.F.Edwards constructed a series of Venn diagrams for higher numbers of sets by segmenting the surface of a sphere. For example, three sets can be easily represented by taking three hemispheres of the sphere at right angles (x = 0, y = 0 and z = 0). A fourth set can be added to the representation by taking a curve.

                             

Author: Navdeep Singh Momi

Group Members 

1. Navdeep Singh Momi
2. Navneet Singh
3. Shyam Pandule
4. Pankaj Ruplani
5. Praloy saha