Venn Diagram

Concept & Uses

Venn Diagrams are used to show logical relationships between different sets or groups using circles. It's a crucial topic in reasoning for SSC, Railway, HSSC, and other competitive exams.

• Each circle represents a category or group.
• Overlapping circles show common elements between sets.
• Non-overlapping circles represent disjoint sets.

Types of Venn Diagrams

• Simple Venn Diagram (2 sets) – Eg: Men and Doctors
• Three Set Diagram – Eg: Students, Boys, Cricketers
• Number-Based Venn Diagrams – Used to solve numerical problems involving sets

Important Rules

• Always read the options with logical mapping in mind.
• Use elimination to find the correct Venn relationship.
• Use the following formula for numerical Venn:
  Total = Only A + Only B + Only C + A ∩ B + B ∩ C + A ∩ C – 2 × A ∩ B ∩ C + None

Previous Year Questions with Solutions

1. SSC CHSL 2023: Which diagram best represents the relationship among "Birds", "Crows", and "Dogs"?
   Solution: Crows ⊂ Birds, Dogs are separate → Correct Venn has Birds as large circle, Crows inside, Dogs separately.
2. RRB NTPC 2021: In a group of 100 people, 60 like Tea, 40 like Coffee, and 20 like both. How many like only Tea?
   Solution: Only Tea = 60 – 20 = 40
3. SSC CGL 2020: Select the correct Venn diagram for "Musicians", "Singers", "Painters".
   Solution: Some may be common, others may be different → Three intersecting circles
4. HSSC 2019: Which Venn diagram shows the relationship among "Women", "Mothers", "Engineers"?
   Solution: All mothers are women, some women are engineers → Overlapping circles
5. SSC MTS 2018: Identify the diagram representing "Fruits", "Mango", "Vegetables".
   Solution: Mango ⊂ Fruits, Vegetables are separate → Mango inside Fruits, Vegetables separate