# Venn Diagram: Overview, Questions, Preparation

Sets 2021 ( Sets )

2.1K Views
This chapter has multiple topics listed below:

Rachit Kumar SaxenaManager-Editorial

Updated on Apr 15, 2021 10:10 IST

## What are Venn Diagrams?

Venn diagrams are essential pictorial representations of sets using circles. They are used to represent individual sets and depict operations between sets and showcase relations between two or more sets. They were first introduced by John Venn in the 19th Century, and are also called set diagrams or logic diagrams. Set operations such as union and intersection, as well as arithmetic operations such as addition and subtraction.

Sets are fundamental to the wide world of statistics. Though seemingly simple, the Set Theory is used widely for statistical analysis and representation of large groups of data. It is imperative that students gain a firm grasp over the set theory, and the various topics included in it, at a very early stage. For many students, the set theory is synonymous with Venn diagrams.

Venn diagrams are a significant part of the set theory, and this is very evident from the way in which they are explained in the NCERT Mathematics Textbook of Class XI. The process of drawing Venn diagrams is explained from scratch, using one, two, and three sets. Further in the chapter, Venn diagrams are used wherever possible to explain set theorems and operations. From the exam point of view, Venn diagrams are essential in almost every set theory-related question you will attempt. The individual weightage of drawing Venn diagrams in these questions might be less, but they can be an essential step in both 4 marks and 6 mark questions. Application-based questions concerning the Set Theory almost necessarily involve the usage of Venn diagrams for the explanation.

Set Operations Using Venn Diagrams

Image Source: NCERT

Venn diagrams can also be used to show subsets and complements of sets. In a Venn diagram, it isn’t just the circles that depict the sets that are important. The box that encloses these circles is also a part of the Venn diagram and is equally important. This is because the region interior to this box represents the universal set.

Using the Venn diagram, you cannot just depict the complements of individual sets, but also the complements of unions and intersections of two or more sets. These are difficult to express using set equations, but Venn diagrams make them easier.

Importance and Weightage

Venn diagrams are a significant part of the set theory, and this is very evident from the way in which they are explained in the NCERT Mathematics Textbook of Class XI. The process of drawing Venn diagrams is explained from scratch, using one, two, and three sets. Further in the chapter, Venn diagrams are used wherever possible to explain set theorems and operations. From the exam point of view, Venn diagrams are essential in almost every set theory-related question you will attempt. The individual weightage of drawing Venn diagrams in these questions might be less, but they can be an essential step in both 4 marks and 6 mark questions. Application-based questions concerning the Set Theory almost necessarily involve the usage of Venn diagrams for the explanation.

## Illustrated Examples of Venn Diagram

1. Set A is the set of all non-negative real numbers. Set B is the set of whole numbers. What is the intersection of A and B?
Solution. The intersection of A and B is the number 0.

If Set A has 10 elements, Set B has 4 elements, and both sets have 2 elements in common, how many elements does the union of A and B have?
The union of A and B has n(A) + n(B) - n(AB) elements
= 10 + 4 - 2
= 12

2. What is the complement of the set of rational numbers, if the universal set is the set of real numbers?
Solution. The complement of the set of rational numbers is the set of irrational numbers.

## FAQs for Venn Diagram

Q: What set operations can be expressed using a Venn diagram?

A: The union, intersection, and complement of sets can be expressed using a Venn diagram.

Q: What is the box in a Venn diagram?

A: The box is an important part of the Venn diagram, and represents the universal set.

Q: How can you depict the complement of a set using a Venn diagram?

A: The area inside the box, apart from the set itself, is the complement of the set.

Q: How can you depict disjoint sets in a Venn diagram?

A: Two circles in a Venn diagram that do not have any common area can be said to be disjoint sets.

Q: How do you express the intersection of two sets in a Venn diagram?

A: The area common to two circles in a Venn diagram can be said to be the intersection of the sets they represent.

## News & Updates

Latest NewsPopular News

### NDA 1 Answer Key 2024 (OUT) Live Updates: Download Answer Key for Maths & GAT (Set A,B,C,D)

Anangsha PatraApr 21, 2024 23:02 IST

### CBSE Result 2024 Class 10, 12 @cbse.nic.in; Live Updates on Date & Time

Anum AnsariApr 21, 2024 23:02 IST

### TS Inter Results 2024 (Today?) @tsbie.cgg.gov.in; Live updates

Anum AnsariApr 21, 2024 23:00 IST

### JEE Main Marks vs Percentile vs Rank 2024: Calculate Percentile and Rank Using Marks

Satyendra SinghApr 21, 2024 20:38 IST

### NEET Chapter Wise Weightage 2024 PDF by NTA: Physics, Chemistry & Biology

Sreetama Datta RoyApr 18, 2024 16:42 IST

### List of NIT Colleges in India 2024 - NIRF Ranking, Courses, Seats, Cutoff, Fees and Placement

Satyendra SinghMar 8, 2024 16:43 IST

### JEE Main 2024 Chapter wise Weightage: Physics, Chemistry & Mathematics

Satyendra SinghApr 8, 2024 08:36 IST

### TET 2024: Notification, Exam Date, Syllabus, Eligibility & Results

Rupali PruthiApr 17, 2024 09:34 IST

Sets Exam

### Student Forum

Anything you would want to ask experts?
Write here...

Answered a month ago

The M.A. in Mass Communication programme at IILM University stands out for its hands-on approach, integrating theoretical knowledge with practical assignments like portfolio creation, short films, and research projects. It offers specialised tracks in Print Media, Electronic Media, Corporate Communi

...more

S

Samir Bhardwaj

Contributor-Level 7

Answered 2 months ago

The Staff Selection Commission conduct the SSC MTS Tier 1 exam online as a Computer-Based Exam (CBE). The SSC MTS exam is conducted in multiple shifts and Commission conduct normalisation of the marks to prepara a Common Merit List. The Commission release the SSC MTS answer key for each candidate se

...more

Rachit Kumar Saxena

Contributor-Level 10