Wednesday, February 20

Venn diagram

An illustrative representation of relationship between and among the given sets that have something in common are called Venn Diagrams. These diagrams are represented using circles, the most commonly used ones are the two circles and three circle Venn-diagrams. It is used mainly to depict the intersections of sets which mean to show the objects or things common to all the sets. The Picture of Venn diagram with two circles or three circles consists of a rectangle which has in it two circles or three circles respectively. Intersection of sets is shown as overlapping circles, if no common objects then the circles are shown separately.

The total number of elements in the set is shown at the right corner of the rectangle using a symbol ‘ยต’ or ‘E’. The object or elements which do not belong to any of the sets is shown outside the circle within the rectangle. A glance at the Venn diagram help to understand the complete picture of the relationship among the sets given and also help to find the unknowns values using  the diagram.

Example of Venn Diagram is as follows: set X={1,2,3,5,7,9} and set Y={7,9,11,13}, the intersection of these sets given by X∩Y={7,9}.
The Venn-diagram showing the relationship between these two sets is as given below, the pink region shows the intersection of the sets, X∩Y.It also shows the elements only in the set X {1,3,5} in green color and the elements only in the set Y {11,13} in yellow color.

Venn diagram compare and contrast the relationship between the elements of the sets, they are basically used to visualize the relationship between two or three sets. They are also used to compare and contrast the characteristics of the elements of the sets.  An outline about the sets can be easily created using the Venn-diagrams. Venn Diagram with three circles is a type of diagram which involves three sets.  Let us learn more about this using a simple example: A survey was done on a group of children as how many like to play baseball, football and ice hockey shown by the Venn-diagram below,

The above Venn-diagram gives the following information about the three sets, F, B and I.

  • Total number of children (E) would be sum of all the numbers on the three circles, 5+14+8+2+16+5+20=70, so E=70.
  • n(F)=29, n(B)=47, n(I)=31
  • only n(F)=5, only n(B)=20, only n(I)=16
  • n(F∩B∩I)=8, n(F∩B)=22, n(B∩I)=13, n(F∩I)=10
  • only n(F∩B)=14, only n(B∩I)=5, only n(F∩I)=2

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