Venn Diagram - Definition, Problems with Solutions, Examples

In the competitive exam, some students don't understand venn diagram questions or problems because maybe they don't know properly about venn diagram topic. So, here I am sharing you venn diagram definition, venn diagram problems with solutions from which you can understand this topic properly.

In this blog, given you different-2 examples with their types which can help you to easily practice for your competitive exams.

Understand Venn Diagram topic in Detail

Definition of Venn Diagram 

The process of presenting things/numbers through the diagrammatic medium form the given group of elements is called Venn diagram.

According to its characteristics, Venn diagram may be categorized in two types:

1. Identification of Class through circle

2. Identification of Class Through Numbers and Letters.

1. Identification of Class Through Circle.

A class is a group or collection of objects all having something as common. In this type, Venn diagrams are used to establish relationship between the given groups. Generally, an independent diagram is used to represent a different class. Candidates are required to identify the Venn diagram, which most correctly establish a relation between the given objects.

Keep In Mind

● Concept of group of class.

● Diagrammatic representation of classes like individual and common.

● The individual diagram for any of the class then corelate the diagram, if belongs to group.

Ex.1. Which of the following diagram represents the relationship among paper, Stationary and Ink?

Answer : B

Solution:

Both ‘Paper’ and ‘Ink’ are type of stationary but both are different.

Ex.2. Which of the following diagram represents the relationship among polygons, Rhombus and Quadrilaterals?

Answer : D

Solution:

Both Rhombus and Quadrilaterals are Polygons and all Quadrilaterals are Polygons also.

Identification of Class Through Numbers and Letters

2. Identification of class through numbers and letters 

In these types of questions, more than one geometrical figure represents different classes with the specified numbers or letters. Candidates are required to analyse the figure carefully and then answer certain question as per the given information.

Keep in Mind

● Only A = P            ● A = P + r          ● Only B = Q

● B = Q + r                ●  A ꓵ B = r         ● A ꓴ B = P + Q – r

● A + B = P + Q + 2r                             ● A – B = P + Q

Ex.1. How many educated people are employed?

(A) 18

(B) 16

(C) 24

(D) 26

Answer :A

Solution:

Number of educated people who are employed = 6 + 12 = 18

Ex.2. Find out the number of people who don’t play any game?

(A) 19

(B) 24

(C) 29

(D) 21

Answer :C

Solution:

Number of people playing at least one game

= 16 + (25 - 16) + (22 – 16)

= 16 + 9 + 6

= 31

Number of people not playing any game

= 60 – 30

= 29.

Important Notes:

While solving such question candidate must keep in mind such basics of venn diagram

● The given diagram shows that a class is totally inserted in another, but not mixed.

● The given diagram shows that no one class is distribution in anyone but they are partly related to each other.

● The given diagram shows that there is no relation between two classes and no elements are common.

● Here, P union Q means that all the elements of P and Q will include in a new set.

● Here, P intersection Q means that all the common properties of P and Q will include a new set

Feel free and ask me anything in the comment section, if you face any difficulty in venn diagram blog.