In this guide
A Venn diagram uses circles to show how groups are related. One circle is one group. Where circles overlap, some members belong to both groups. Where one circle sits inside another, every member of the small group belongs to the big one.
SSC GD asks two kinds of Venn question. The first gives three words, such as Doctors, Women and Mothers, and asks which diagram shows how they relate. The second gives numbers in a simple diagram or a sentence and asks you to count: how many like both, how many like neither. Both kinds appear regularly in the reasoning section, and both are quick once you have the basics.
Three basic pictures
Every Venn diagram is built from three ways two groups can relate.
| Picture | Meaning | Example |
|---|---|---|
| One circle inside another | Every member of the small group belongs to the big group | Rose inside Flower |
| Overlapping circles | Some members belong to both, and each group has members of its own | Teachers and Women |
| Separate circles | No member belongs to both | Dogs and Cats |
The two-question method
For three words, take them in pairs. There are only three pairs. For each pair, ask two questions.
- Is every A a B (or every B an A)? If yes, one circle goes inside the other.
- If not, can something be both? If yes, the circles overlap. If no, they are separate.
Put the three answers together and pick the diagram that matches all of them.
Eight three-group patterns
| Groups | How the circles sit |
|---|---|
| Amritsar, Punjab, India | Three circles, each inside the next |
| Cricket, Hockey, Sport | Two separate circles inside a bigger one |
| Men, Doctors, Human beings | Two overlapping circles inside a bigger one |
| Rose, Flower, Chair | Rose inside Flower; Chair separate from both |
| Mothers, Women, Doctors | Mothers inside Women; Doctors overlapping both |
| Men, Women, Doctors | Men and Women separate; Doctors overlapping both |
| Dog, Cat, Cow | Three separate circles |
| Students, Players, Singers | Three circles, all overlapping each other |
Solved examples
Example 1 (choose the diagram). Soldiers, Men, Fathers
- Fathers and Men: every father is a man. Fathers go inside Men.
- Soldiers and Men: some soldiers are men, and some are women. Overlap.
- Soldiers and Fathers: some soldiers are fathers. Overlap.
- Answer: Fathers inside Men, with Soldiers overlapping both.
Example 2 (choose the diagram). Men, Women, Doctors
- Men and Women: no one is both. Separate.
- Doctors and Men: some doctors are men. Overlap.
- Doctors and Women: some doctors are women. Overlap.
- Answer: two separate circles, with a third circle overlapping both.
Example 3 (counting, neither). In a class of 40, 25 students like tea, 20 like coffee and 10 like both. How many like neither?
- Students who like at least one = tea + coffee − both = 25 + 20 − 10 = 35.
- We subtract "both" once because those 10 were counted in tea and again in coffee.
- Neither = 40 − 35 = 5.
Example 4 (counting, only one). In the same class, how many like only tea, and how many like only coffee?
- Only tea = 25 − 10 = 15.
- Only coffee = 20 − 10 = 10.
- Check: 15 + 10 + 10 (both) + 5 (neither) = 40. It adds up.
Example 5 (finding the total). In a group, 18 people speak Hindi, 12 speak English and 5 speak both. Everyone speaks at least one of the two. How many people are in the group?
- Total = 18 + 12 − 5.
- Answer: 25.
Example 6 (reading regions). A survey of 50 people about three newspapers, A, B and C, gives these counts.
| Region | People |
|---|---|
| Only A | 10 |
| Only B | 8 |
| Only C | 6 |
| A and B, not C | 5 |
| B and C, not A | 4 |
| A and C, not B | 3 |
| All three | 2 |
How many read exactly two newspapers? How many read A? How many read none?
- Exactly two: 5 + 4 + 3 = 12. "All three" is not included.
- Read A: every region inside A's circle: 10 + 5 + 3 + 2 = 20.
- Read at least one: 10 + 8 + 6 + 5 + 4 + 3 + 2 = 38. None: 50 − 38 = 12.
Common mistakes
| Mistake | Correct way |
|---|---|
| Putting a group inside another when only some members belong | Inside means every member, with no exceptions |
| Showing Men and Women as overlapping | No one is in both; they are separate |
| Adding the two groups without subtracting "both" | At least one = A + B − both |
| Counting "all three" in "exactly two" | Exactly two means two and not the third |
| Checking only two of the three pairs | Check all three pairs before choosing |
Practice set
- Which diagram shows Delhi, India, Asia?
- Which diagram shows Cow, Goat, Animal?
- Which diagram shows Engineers, Women, Singers?
- Which diagram shows Sparrow, Bird, Table?
- In a group of 50, 30 play cricket, 25 play football and 10 play both. How many play neither?
- In the same group, how many play only football?
- In a group where everyone reads at least one of two magazines, 22 read the first, 15 read the second and 7 read both. How many people are in the group?
- Using the newspaper table in Example 6, how many people read B?
Answers:
- Three circles, each inside the next. Delhi is in India, and India is in Asia.
- Two separate circles inside a larger one. Cows and goats are both animals, but no animal is both.
- Three overlapping circles. Some engineers are women, some women sing, and some engineers sing.
- Sparrow inside Bird, and Table separate from both. Every sparrow is a bird; no table is either.
- 5. At least one = 30 + 25 − 10 = 45, so neither = 50 − 45 = 5.
- 15. 25 − 10 = 15.
- 30. 22 + 15 − 7 = 30.
- 19. Only B 8 + A and B 5 + B and C 4 + all three 2 = 19.
What to do next
- Learn the eight patterns until you can sketch each one in a few seconds.
- For every diagram question, write the three pairs and your answer for each before looking at the options.
- Solve 10 diagram and 5 counting questions a day for a week.
- Learn the formula: at least one = A + B − both; neither = total − at least one.
- Move on to syllogism, which uses the same circles with different rules.
A note on dates and numbers. Exam patterns, vacancies and schedules change from year to year. Always confirm the current details in the latest notification on the Staff Selection Commission website .
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