Venn Diagram

Venn Diagram is a topic where circles are used to show the relationship between different groups. You have to find how many members belong to one group, both groups, or neither group. It is a visual and logical topic that is very easy once you understand the basic concepts.

What is a Venn Diagram?

A Venn Diagram uses overlapping circles to show relationships between groups.

• The part inside only Circle A = members belonging to only Group A
• The part inside only Circle B = members belonging to only Group B
• The overlapping part = members belonging to BOTH Group A and Group B
• The part outside both circles = members belonging to NEITHER group

Types of Venn Diagram Questions in SSC CGL:

Type 1 - Relationship Between Three Items Three items are given and you have to find which Venn diagram best represents their relationship.

Example 1: 

Which diagram represents: Dogs, Animals, Cats?

Logic:

• All dogs are animals
• All cats are animals
• No dog is a cat

Example 2: 

Which diagram represents: Teachers, Doctors, Humans?

Logic:

• All teachers are humans
• All doctors are humans
• Some teachers may also be doctors

Example 3:

Which diagram represents: Cricket, Football, Sports?

Logic:

• Cricket is a sport
• Football is a sport
• Cricket and Football are different sports

Type 2 - Data Based Venn Diagram Numbers are given in different parts of circles and you have to calculate totals.

Example: 

In a class of 50 students:

• 30 students like Cricket
• 25 students like Football
• 10 students like both Cricket and Football

Questions that can be asked:

• How many like only Cricket? = 30 - 10 = 20
• How many like only Football? = 25 - 10 = 15
• How many like at least one sport? = 20 + 15 + 10 = 45
• How many like neither? = 50 - 45 = 5

Important Formula:

n(A ∪ B) = n(A) + n(B) - n(A ∩ B)

Where:

• n(A ∪ B) = Total who like at least one
• n(A) = Total in Group A
• n(B) = Total in Group B
• n(A ∩ B) = Total in both groups

Type 3 - Three Circle Venn Diagram Three groups are given with overlapping data.

Example: 

In a group of 100 people:

• 40 know Hindi
• 35 know English
• 30 know Tamil
• 10 know Hindi and English both
• 8 know English and Tamil both
• 6 know Hindi and Tamil both
• 3 know all three languages

Questions:

• How many know only Hindi? = 40 - 10 - 6 + 3 = 27
• How many know at least one language? = 40 + 35 + 30 - 10 - 8 - 6 + 3 = 84
• How many know none? = 100 - 84 = 16

Formula for Three Groups:

n(A ∪ B ∪ C) = n(A) + n(B) + n(C) - n(A ∩ B) - n(B ∩ C) - n(A ∩ C) + n(A ∩ B ∩ C)

Common Relationships in Type 1 Questions:

• Animal inside bigger Animal group: Dog inside Animal circle
• Two completely separate groups inside bigger group: Cricket and Football inside Sports
• Two partially overlapping groups inside bigger group: Male Doctors and Doctors inside Humans
• Completely separate groups with no connection: Sun, Moon, Stars (all separate circles)
• One inside another inside another: Villages inside Districts inside States

How to Solve Venn Diagram Questions:

Step 1 - Read all three items carefully. 

Step 2 - Check if one item is a subset of another (like Dog is a subset of Animal). 

Step 3 - Check if two items can overlap (like a person can be both Teacher and Doctor). 

Step 4 - Check if two items are completely separate (like Cricket and Football). 

Step 5 - Choose the diagram that matches all three relationships.

For Data Based Questions:

Step 1 - Write down all given values. 

Step 2 - Draw a Venn diagram and fill in the overlapping part first. 

Step 3 - Calculate only A = Total A minus both. 

Step 4 - Calculate only B = Total B minus both. 

Step 5 - Add all parts to find total.

Important Tips:

• In Type 1 questions always check if a subset relationship exists first
• Remember the formula n(A ∪ B) = n(A) + n(B) - n(A ∩ B)
• Always fill in the innermost overlapping region first in data questions
• 2 to 3 questions come from this topic in SSC CGL every year
• Practice drawing Venn diagrams for at least 10 different relationships daily