Venn Diagrams
About 6 min · General Intelligence and Reasoning · English
Time worked out from the lesson's 368 words at 150 words a minute, plus a minute for each question.
These questions test your ability to understand how groups overlap and to identify which diagram correctly represents a given relationship between categories.
Key ideas
- Disjoint sets — Two or more categories with no common members. Example: Dogs, Cats, Birds are three separate circles with no overlap.
- Subset relationship — One category is completely contained within another. Example: Roses are a subset of Flowers; the Roses circle sits entirely inside the Flowers circle.
- Overlapping sets — Two categories share some members but each has unique members too. Example: Students and Athletes overlap (student-athletes exist), but not all students are athletes and not all athletes are students.
- Concentric circles — Used when all members of category A are also members of category B, which are all members of category C. Example: Sparrows ⊂ Birds ⊂ Animals appears as three nested circles.
- Three-way intersections — When three sets A, B, C are given, there can be regions where only A and B overlap, only B and C overlap, only A and C overlap, or all three overlap simultaneously. Count these regions carefully.
Quick reference
- All disjoint → Three separate circles with no contact (Dogs, Cats, Birds).
- One inside another → Subset relationship; small circle inside big circle (Rose ⊂ Flower).
- Two overlap, one separate → Common for professions vs. objects (Teachers/Writers overlap, Pen separate).
- All three overlap → Possible when all categories can coexist in one person (Indian/Woman/Engineer).
- Concentric circles → Hierarchical containment; smallest inside middle inside largest (Sparrow ⊂ Bird ⊂ Animal).
Check yourself: 3 questions
1. In a class of 60 students, 35 students play cricket, 30 students play football and 20 students play both cricket and football. How many students do not play either cricket or football?
2. In a survey of 100 people, 65 like tea, 45 like coffee, and 25 like both tea and coffee. How many people like only tea?
3. In a group of 120 students, 70 students study Mathematics, 60 students study Physics, 50 students study Chemistry, 30 students study both Mathematics and Physics, 25 students study both Physics and Chemistry, 20 students study both Mathematics and Chemistry, and 10 students study all three subjects. How many students study exactly one subject?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 18 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.
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