Patwari Exam · Reasoning
Venn Diagrams & Logical Diagrams
This note explains union, intersection, and statement-conclusion questions using Venn and logical diagrams.
- Reasoning & Numerical Ability
- 5 min read
Verified 6 October 2026
Key Formulas & Methods
- Venn diagram basics
- In a Venn diagram, circles represent sets; overlap = shared members.
- Union and intersection
- A∪B = A+B−A∩B (union); A∩B = shared members (intersection).
- Worked example
- Example: 30 students study Hindi, 25 study English, 10 study both → only Hindi = 20, only English = 15, total = 45.
- Three-set formula
- Three circles: A∪B∪C = A+B+C−A∩B−B∩C−A∩C+A∩B∩C.
- Logical diagram statements
- Logical diagram questions: "All A are B" → A is entirely inside B; "Some A are B" → partial overlap.
- Checking conclusions
- Checking conclusions: look at the diagram to see whether the statement is true or not.
- Exam tip
- Exam tip: always draw an Euler/Venn diagram; fill in the numbers in each region.
Frequently Asked Questions
How do you find the union and intersection in a Venn diagram?+
Union A∪B = A+B−A∩B, where A∩B represents the shared members (intersection).
What is the difference between "All A are B" and "Some A are B"?+
In "All A are B", A lies entirely inside B, while in "Some A are B" there is only a partial overlap between the two.
What is the formula for a three-set Venn diagram?+
For three circles, the total is found using A∪B∪C = A+B+C−A∩B−B∩C−A∩C+A∩B∩C.