Venn diagram





Venn diagram is a graphical representation of sets and relation between sets. Venn diagram is the diagram which shows the possible relations between the finite collections of set. Venn diagram was introduced in 1880 by john Venn. It is constructed by more than two circles which is generally overlapping . To draw the Venn diagram, you first draw the rectangular which is called “universe” then you draw the required quantity of circle for the collection of set. Whole elements of the set are inside the universe. The elements which are in universe and are not in sets then these elements are place outside the circle but inside the universe. The interior of the circle represent the element of the set while exterior represent the element that are not the member of that sets. The overlapping area or intersection would represent the common element of the sets. Generally venn diagram contains two and three sets. By using the venn diagram student can easily solve complex problems. Venn diagram can be used to illustrate both sets relationship and logical relationships. It is used in scientific and engineering presentations, in theoretical mathematics, in computer applications, and in statistics. The following venn diagram shows the relationship existing between three sets. Students can use venn diagram to compare two things, people, place etc.

venn diagram

For example, the order three diagrams consist of three mutually intersecting circles with eight regions. The region A, B and C consists of members which are only in one set not in others. The three regions A \bigcap B, B \bigcap C, and A \bigcap C consist of members which are in two sets but not in three. A \bigcap B \bigcap Cconsists of member which are in all three sets and no region occupied represents \phi .

Some of examples of venn diagram showing relation between sets are given below:-

The Venn diagram above represents B?A or set B is subset of set A.

The Venn diagram above represents A=B or set A is equal to set B.

The Venn diagram above represents that set A and set B are disjoint set.

The Venn diagram above represents that set A and set b are intersecting.

 

The Venn diagram above represents following things:
a> Set A and set B are intersecting.
b> Set B and set C are intersecting.
c> Set C and set A are intersecting.
d> Set A , B and C are also intersecting.



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