Logical Venn Diagram

Venn Diagram

Venn diagram is a way of representing sets pictorially.

This idea was developed by John Venn, an English Mathematician. A set is a collection of well-defined objects, called the elements of the set

Representation of different sets
(A) Subset: If one kind of item is completely included in the other.

Example:

(C) Intersection of two sets: If one Kind of item is partially included in other one.

Some females are doctors. Some doctors are females.

(D) Intersection of three sets: If items are partially included in others.

Some dogs and cats are pets;not all. Some pets are neither dogs nor cats.
(E) If the three items are partly related to each other, they are represented as shown in the adjoining figure. Ex: Clerks, Government Employees, Educated Persons

Clearly, some clerks may be government employees and some may be educated.Similarly, some government employees may be clerks and some may be educated. Also, some educated persons may be clerks and some may be government employees. So, the given items may be represented as shown in the following figure with three different circles denoting the three classes.

(F) If one item belongs to the class of second and the third itemis partly related to these two, they are represented as shOwn alongside. Ex: Females, Mothers,Doctors
Clearly, allmothers are females. Tllis would be represented by two concentric circles. But,some females and some mothers can be doctors. So, the circle representing doctors would intersect the two concentric circles. Thus, the diagram becomes as shOwn in the following figure with circle
A representing Motllers, circle B representing Females and circle C representing Doctors.