Venn Diagrams - Introduction and Examples (with Solutions) Quant Notes | EduRev

IBPS Clerk Prelims - Study Material, Mock Tests

CAT : Venn Diagrams - Introduction and Examples (with Solutions) Quant Notes | EduRev

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What is a Venn Diagram?

  • A Venn diagram (also called a set diagram or logic diagram) is a diagram that shows all possible logical relations between a finite collection of different sets.
    Venn Diagrams - Introduction and Examples (with Solutions) Quant Notes | EduRev
    Venn Diagram
  • Typically overlapping shapes, usually circles, are used, and an area-proportional or scaled Venn diagram is one in which the area of the shape is proportional to the number of elements it contains. 
  • These diagrams represent elements as points in the plane and sets as regions inside curves. An element is in a set S just in case the corresponding point is in the region for S. They are thus a special case of Euler diagrams, which do not necessarily show all relations. 
  • Venn diagrams were conceived around 1880 by John Venn. They are used to teach elementary set theory, as well as illustrate simple set relationships in probability, logic, statistics, linguistics and computer science.
Examples
  • In the following figure, the small square represents the persons who know English, the triangle represents those who know Marathi, the big square represents those who know Telugu and the circle represents those who know Hindi. 
  • In the figure, different regions from 1 to 12 are given.

Venn Diagrams - Introduction and Examples (with Solutions) Quant Notes | EduRev

Q1. How many persons can speak English and Hindi both languages only?
A. 5
B. 8
C. 7
D. 18

Correct Answer is Option (A).

  • Number of persons who can speak English and Hindi both only is 5.

 

Q2. How many persons can speak Marathi and Telugu both?

A. 10

B. 11

C. 13

D. None of these

Correct Answer is Option (C).

6 + 7 = 13.


Q3. How many persons can speak only English?
A. 9
B. 12
C. 7
D. 19

Correct Answer is Option (B).

  • Number of persons were can speak English is 12.

 

Q4. How many persons can speak English, Hindi and Telugu?
A. 8
B. 2
C. 7
D. None of these

Correct Answer is Option (B).

  • Number of persons who can speak English, Hindi and Telugu is 2.

 

Q5. How many persons can speak all the languages?
A. 1
B. 8
C. 2
D. None

Correct Answer is Option (D).

  • There is no such person who can speak all the languages.
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