Logical Venn Diagram Notes for SSC Exams

Logical Venn diagram questions ask you to choose the diagram of circles that best shows the relationship between three given words, for example Dog, Mammal, Animal. A Venn diagram uses circles to show how groups are related: one group may lie fully inside another, two groups may overlap, or they may be completely separate. Venn questions are asked in many SSC Reasoning papers, and there are only a few standard figures to remember. These Venn diagram notes for SSC explain every standard figure with examples, number-based Venn problems with formulas, and practice questions.

What Is a Venn Diagram?

• A Venn diagram shows the relationship between groups (sets) using circles.
• A circle inside another circle means that the first group is a part of the second group.
• Two circles that overlap mean that some members belong to both groups.
• Two circles that are apart mean that no member belongs to both groups.

Standard Relationships and Their Figures

How to Choose the Right Diagram

1. Find the biggest group among the three words. Put it in the outer circle.
2. Check whether each smaller group is fully inside it, or only partly.
3. For every pair of words, ask "Can one member belong to both groups?" If yes, the circles overlap. If no, they are separate.
4. If a word cannot belong to the other two groups at all, draw it as a separate circle.
5. Match your figure with the options and choose the same one.

Solved Examples on Word Relationships

Example 1. Which diagram shows Dog, Mammal, Animal?
Every dog is a mammal, and every mammal is an animal. Answer: three concentric circles, with Dog in the smallest circle.

Example 2. Which diagram shows Pen, Pencil, Stationery?
A pen is not a pencil, so they are separate. Both are stationery. Answer: two separate circles inside one bigger circle.

Example 3. Which diagram shows Doctors, Women, Mothers?
All mothers are women, so the Mothers circle is inside the Women circle. Some women and some mothers are doctors, but not all, and some doctors are men. Answer: a small circle (Mothers) inside a bigger circle (Women), and a third circle (Doctors) overlapping both.

Example 4. Which diagram shows Sun, Moon, Earth?
They are different objects and no one object belongs to the other group. Answer: three separate circles.

Example 5. Which diagram shows Singers, Dancers, Artists?
A person can be both a singer and a dancer, and both are artists. Answer: two overlapping circles inside a bigger circle.

Number-Based Venn Problems

In these questions, the numbers of people in different groups are given, and you have to find how many belong to one or more groups. Use these formulas.

Example 6. In a class of 60 students, 35 like tea, 28 like coffee and 10 like both. How many like neither?
Tea or coffee = 35 + 28 − 10 = 53. Neither = 60 − 53 = 7. Students who like only tea = 35 − 10 = 25, and only coffee = 28 − 10 = 18.

Example 7. In a group of 100 persons, 72 speak Hindi and 43 speak English. Everyone speaks at least one language. How many speak both?
Both = 72 + 43 − 100 = 15.

Quick Tips

• Do not use your own knowledge about rare cases. Think of the normal, general relationship between the words.
• If one word can include the other two, draw the biggest circle for it.
• If two words can overlap, never draw them separate.
• In number problems, first mark the number in "both" and then work outward.
• Check your answer by adding all the parts of the diagram. The sum should equal the total.

Quick Revision Points

• A circle inside a circle means a part of the other group.
• Overlapping circles mean some common members.
• Separate circles mean no common members.
• n(A or B) = n(A) + n(B) − n(A and B).
• Neither = Total − n(A or B).

Practice Questions With Answers

1. Which diagram shows Dog, Mammal, Animal?
   Answer: Three concentric circles.
2. Which diagram shows Pen, Pencil, Stationery?
   Answer: Two separate circles inside one bigger circle.
3. Which diagram shows Doctors, Women, Mothers?
   Answer: Mothers inside Women, and Doctors overlapping both.
4. Which diagram shows Mumbai, Maharashtra, India?
   Answer: Three concentric circles (Mumbai in Maharashtra in India).
5. Which diagram shows Sun, Moon, Earth?
   Answer: Three separate circles.
6. In a class of 50, 30 play cricket and 25 play football, and 5 play neither. How many play both?
   Answer: 10 (30 + 25 − 45).
7. Of 80 students, 50 take Maths and 40 take Science. Every student takes at least one. How many take both?
   Answer: 10 (50 + 40 − 80).
8. In a town, 60% read newspaper A, 50% read newspaper B and 20% read both. What percentage read neither?
   Answer: 10% (union = 60 + 50 − 20 = 90%).
9. Which diagram shows Men, Women, Human beings?
   Answer: Two separate circles inside one bigger circle.
10. Which diagram shows Singers, Dancers, Artists?
    Answer: Two overlapping circles inside a bigger circle.

How to Practise This Chapter

Practise five Venn questions daily, and draw the circles on paper each time. Then attempt timed sets from our practice papers and check how Venn diagrams appear in actual exams on the previous year papers page. Read Mathematical Operations before this chapter, and revise the full reasoning list from Coding-Decoding to test your overall preparation.

Explore More SSC Subjects

SSC exams test many subjects, so connect this topic with the related subjects below:

• Quantitative Aptitude Notes
• English Notes
• General Awareness Notes
• Computer Knowledge Notes
• Stenography Notes
• All SSC subjects and notes

Frequently Asked Questions

What is a logical Venn diagram?

A logical Venn diagram is a reasoning topic in which you choose the figure of circles that correctly shows the relationship between three given words or groups.

How many Venn diagram questions come in SSC exams?

Usually one or two Venn diagram questions come in the Reasoning section of SSC CGL, CHSL, MTS and GD papers, but the number changes from year to year.

What does a circle inside another circle mean?

It means that every member of the smaller group belongs to the bigger group, such as dogs inside animals.

What do overlapping circles show?

Overlapping circles show that some members belong to both groups, such as some women being doctors.

What do separate circles show?

Separate circles show that the two groups have no common members, such as pens and pencils.

How do I decide which word is the biggest group?

The biggest group is the word that can include the other words. For example, among Dog, Mammal and Animal, the word Animal includes all the others.

What is the formula for two groups in number-based Venn problems?

The total in A or B equals n(A) plus n(B) minus n(A and B). Subtract this from the total to find how many belong to neither group.

How do I find the people who belong to only one group?

Subtract the number of people in both groups from the number in that group. For example, only A = n(A) − n(A and B).

Why do I get Venn diagram questions wrong?

Common reasons are using personal knowledge about rare cases, ignoring that two groups can overlap, and drawing the biggest group inside a smaller group.

How can I solve Venn questions faster?

Memorise the eight standard figures, ask whether any member can belong to both groups for each pair of words, and choose the figure that matches.

Do I need to draw the diagram on paper?

For simple questions you can see the figure mentally, but for number-based problems and for three overlapping groups it is better to draw circles and write numbers inside them.

Can the same word be inside two different circles?

Yes. If a group belongs to two different bigger groups, it can lie in the overlapping part of the two circles.

Is Venn diagram the same in Hindi medium papers?

Yes. The figures and the logic are the same. Only the words used in the question are written in Hindi.