Venn Diagrams
About 6 min · General Intelligence and Reasoning · English
Time worked out from the lesson's 404 words at 150 words a minute, plus a minute for each question.
Venn diagrams are a visual method to represent relationships between different sets or groups. In RRB NTPC, this topic tests your ability to understand overlapping categories and calculate elements in various regions of circles representing sets.
Key ideas
- Set: A collection of distinct objects or elements. Denoted by capital letters like A, B, C.
- Universal Set (U): The superset containing all elements under consideration. In diagrams, represented by a rectangle enclosing all circles.
- Intersection (A ∩ B): Elements common to both sets A and B. Shown by the overlapping region of two circles. "Students who play both cricket AND football."
- Union (A ∪ B): All elements in A or B or both. The combined area covered by both circles. "Students who play cricket OR football or both."
- Complement (A'): Elements in the universal set but NOT in A. The region outside circle A but inside the rectangle.
Watch out for
- Double-counting the intersection: Adding n(A) + n(B) without subtracting n(A ∩ B) overcounts shared elements. Always subtract overlaps once. Fix: Use the union formula n(A ∪ B) = n(A) + n(B) − n(A ∩ B).
- Confusing "only A" with "A": "Students who play only cricket" excludes those who also play football, while "students who play cricket" includes everyone in the cricket circle. Fix: "Only A" = n(A) − n(A ∩ B); "A" = entire circle A.
- Wrong order in three-set problems: Trying to calculate outer regions before finding the center region leads to errors. Fix: Always start with n(A ∩ B ∩ C), then pairwise-only regions, then single-set-only regions.
Quick reference
- Two-set union: n(A ∪ B) = n(A) + n(B) − n(A ∩ B)
- None: Total − Union of all sets
- Only A in 2-set: n(A) − n(A ∩ B)
- Three-set: Always fill center n(A∩B∩C) first, then work outward
- Exactly one = Sum of three "only" regions
Check yourself: 3 questions
1. In a group of 80 students, 45 students play cricket, 35 students play football, and 20 students play both cricket and football. How many students play neither cricket nor football?
2. In a class of 100 students, 60 students read English newspapers, 50 students read Hindi newspapers, and 30 students read both English and Hindi newspapers. How many students read only English newspapers?
3. In a survey of 200 people, 120 like tea, 90 like coffee, and 70 like both tea and coffee. How many people like at least one of tea or coffee?
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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