Active and passive voice: rules for every tense
How the verb changes in each tense, pronoun changes, modals and imperative sentences, with SSC examples.
Study notes
Venn diagram: relationships and region counting
How to show relationships between groups with circles, typical sets asked in SSC, and formulas for counting regions, with examples.
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What Venn diagram questions ask
There are two main types. In the first, you choose the diagram that best shows how three groups are related. In the second, you count or identify the people or items in a region of a given diagram.
Basic relationships
| Relationship | Diagram | Example |
|---|---|---|
| One group inside another | Small circle inside a big circle | Mango, Fruit |
| Three groups, each inside the next | Three circles one inside another | Delhi, India, Asia |
| Partly common | Two overlapping circles | Doctors, Women |
| Nothing common | Two separate circles | Cats, Dogs |
| Two separate groups inside a larger one | Two separate circles inside a big circle | Tennis, Football, Games |
| One group cutting across two separate groups | Two separate circles with a third overlapping both | Men, Women, Teachers |
| All three partly common | Three mutually overlapping circles | Singers, Dancers, Actors |
Method for choosing a diagram
- Take the groups two at a time: A and B, B and C, A and C.
- For each pair, ask: is one inside the other, do they overlap, or are they separate?
- Combine the three answers into one diagram and match it with the options.
Example: Mothers, Women, Doctors. Every mother is a woman, so the Mothers circle sits inside the Women circle. Some women are doctors and some doctors are men, so the Doctors circle overlaps the Women circle and also cuts the Mothers circle (some mothers are doctors).
Counting regions
Two sets: n(A ∪ B) = n(A) + n(B) − n(A ∩ B)
Three sets: n(A ∪ B ∪ C) = n(A) + n(B) + n(C) − n(A ∩ B) − n(B ∩ C) − n(A ∩ C) + n(A ∩ B ∩ C)
Neither = Total − n(A ∪ B)
Three sets: n(A ∪ B ∪ C) = n(A) + n(B) + n(C) − n(A ∩ B) − n(B ∩ C) − n(A ∩ C) + n(A ∩ B ∩ C)
Neither = Total − n(A ∪ B)
- Two overlapping circles make 3 regions inside, plus the outside region.
- Three overlapping circles make 7 regions inside, plus the outside region.
- “Only A” = n(A) − n(A ∩ B) for two sets.
Reading a numbered diagram
Some questions place numbers in each region of shapes such as a circle, a square and a triangle. To answer “how many are in A and B but not in C”, add only the regions that lie inside A, inside B and outside C. Shade the regions lightly before adding.
Shortcut: In counting questions, fill the diagram from the centre outwards: the region common to all groups first, then the two-group overlaps, then the “only” regions. This stops you counting anyone twice.
Common mistakes
- Showing two groups as separate when a few members could belong to both (doctors and women).
- Forgetting that a group can sit inside one circle and still cut across another.
- Adding the overlap twice when finding a total.
Solved examples
- Which diagram best shows Mothers, Women and Doctors?
Mothers inside Women; Doctors overlapping both Women and Mothers, with part of Doctors outside Women (male doctors). - Which diagram best shows Delhi, India and Asia?
Delhi is in India and India is in Asia, so three circles one inside another, with Delhi innermost. - In a class of 60 students, 35 like tea, 30 like coffee and 10 like neither. How many like both?
Students who like at least one = 60 − 10 = 50. So 50 = 35 + 30 − both, which gives both = 15.
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