Venn Diagram Questions for SSC CGL: The Short Answer
Venn diagram questions in SSC reasoning give three or more words (like Doctors, Women, Mothers) and ask which diagram of circles shows the relationship between them correctly. To solve one, check each pair of words and decide whether one is fully inside the other, they partly overlap, or they are completely separate, then pick the diagram that matches all three pairs. A second type gives numbers inside a diagram, or a survey, and asks you to count a region using n(A ∪ B) = n(A) + n(B) − n(A ∩ B).
Key takeaway for SSC: SSC CGL, CHSL, MTS and GD ask 1 to 2 Venn diagram questions in reasoning, and RRB NTPC asks them too. Learn the 11 standard diagram types below, always test the three pairs one by one, and remember that "some X are Y" (overlap) is the safest relation when words are general groups of people.
For related reasoning topics, see our syllogism possibility rules note (the same Venn logic in statement form) and blood relation questions for SSC CGL.
What Is a Venn Diagram in Reasoning?
A Venn diagram shows groups (classes) as circles. How the circles touch tells you how the groups relate:
| Relation between two groups | Circles | Example |
|---|---|---|
| One group is completely inside the other (subset) | Small circle inside big circle | Delhi and India |
| The groups share some members (partial overlap) | Two crossing circles | Teachers and Women |
| The groups share no members (disjoint) | Two separate circles | Cats and Dogs |
| Both are exactly the same group | One circle (rare) | — |
Words for people (doctors, women, singers, Indians) usually overlap, because a person can be in both groups. Words for places, parts or levels (city, state, country) usually sit inside each other. Words for different species or opposite kinds (men and women; animals and plants) are separate.
11 Types of Venn Diagram Questions for SSC CGL (with Examples)
| # | Diagram shape | Relationship | Example words |
|---|---|---|---|
| 1 | Three nested circles | A inside B inside C | Delhi, India, Asia |
| 2 | Three separate circles | No common members | Pen, Table, Cow |
| 3 | Three circles in a chain (A meets B, B meets C, A and C apart) | Middle word overlaps both | Men, Doctors, Women |
| 4 | Three circles all crossing | Every pair overlaps | Students, Singers, Dancers |
| 5 | Two separate circles inside a big circle | Two disjoint groups in a bigger group | Animals, Dogs, Cats |
| 6 | Two crossing circles inside a big circle | Two overlapping groups in a bigger group | Humans, Doctors, Engineers |
| 7 | One small circle inside, one separate circle outside | A inside B; C apart from both | Kolkata, West Bengal, Japan |
| 8 | Small circle inside a big one, third circle crossing only the big one | A inside B; C overlaps B but not A | Multiples of 4, Even numbers, Prime numbers |
| 9 | Small circle inside a big one, third circle crossing both | A inside B; C crosses both | Women, Humans, Doctors |
| 10 | Small circle in the overlap of two crossing circles | C is inside both A and B | Women, Parents, Mothers |
| 11 | Two circles crossing, third separate | A overlaps B; C apart | Teachers, Women, Trees |
Note on type 8: every multiple of 4 is even, the prime number 2 is even, but no multiple of 4 is prime. Note on type 10: every mother is both a woman and a parent, while women and parents only partly overlap.
How to Solve Venn Diagram Reasoning Questions (Step-by-Step)
- List the three pairs: A–B, B–C, A–C.
- For each pair, decide one of three relations: inside, overlap or separate. Ask: "Can something be both? Is every A also a B?"
- Draw the circles in that order, starting with the biggest group.
- Match with the options. Only one diagram will fit all three pairs.
Example 1: Doctors, Women, Mothers.
- Doctors–Women: some doctors are women → overlap.
- Women–Mothers: every mother is a woman → Mothers inside Women.
- Doctors–Mothers: some mothers are doctors → overlap.
Diagram: a big Women circle containing Mothers, with Doctors crossing both (type 9).
Example 2: Delhi, India, Asia.
Delhi is in India and India is in Asia → three nested circles (type 1).
Example 3: Men, Doctors, Women.
Men–Doctors overlap, Women–Doctors overlap, Men–Women separate → chain (type 3).
Example 4: Vegetables, Potatoes, Fruits.
Potatoes are vegetables (inside), fruits and vegetables are treated as separate classes in SSC questions, and potatoes are not fruits → one circle inside, one separate (type 7).
Example 5: Animals, Dogs, Cats.
Dogs and cats are both animals but never each other → two separate circles inside one big circle (type 5).
Example 6: Students, Players, Singers.
A person can be a student, a player and a singer at once → three circles all crossing (type 4).
Venn Diagram Questions Based on Numbers (Region Counting)
Here a diagram (or a list) gives numbers in each region, and the question asks for one part such as "how many are doctors but not women".
Use the region labels:
| Region | Means |
|---|---|
| Only A | In A, not in B or C |
| A and B only | In both A and B, not in C |
| All three | Common to A, B and C |
| A but not B | Only A + (A and C only) |
Method: read the question word by word, mark every region that satisfies all the conditions, and add only those numbers.
Example 7: A diagram has three circles: Graduates (G), Employed (E) and Married (M). The numbers are: only G = 12, only E = 9, only M = 15, G and E only = 6, E and M only = 4, G and M only = 7, all three = 3. How many graduates are employed but not married?
Graduates who are employed: G and E only (6) + all three (3). Not married removes the "all three" region. Answer: 6.
How many people are married graduates? G and M only (7) + all three (3) = 10.
Venn Diagram Set Formulas for SSC CGL (Survey Questions)
For two groups:
n(A ∪ B) = n(A) + n(B) − n(A ∩ B), and neither = total − n(A ∪ B).
Example 8: In a class of 60, 35 students like tea, 30 like coffee and 12 like both. How many like neither?
Like at least one = 35 + 30 − 12 = 53. Neither = 60 − 53 = 7.
For three groups:
n(A ∪ B ∪ C) = n(A) + n(B) + n(C) − n(A∩B) − n(B∩C) − n(A∩C) + n(A∩B∩C)
Example 9: Of 100 students, 50 study Hindi, 40 English and 30 Sanskrit; 15 study Hindi and English, 10 English and Sanskrit, 12 Hindi and Sanskrit, and 5 study all three. Find (a) how many study at least one language, (b) none, (c) only Hindi, (d) exactly two.
- (a) 50 + 40 + 30 − 15 − 10 − 12 + 5 = 88
- (b) 100 − 88 = 12
- (c) Only Hindi = 50 − 15 − 12 + 5 = 28
- (d) Exactly two = (15 + 10 + 12) − 3 × 5 = 22
Maximum and minimum overlap: if 40 out of 60 like A and 35 like B, then both is at least 40 + 35 − 60 = 15 and at most the smaller group, 35.
Venn Diagram Tricks and Common Mistakes
| Trap | Correct thinking |
|---|---|
| Treating people groups as separate | Doctors and women overlap: a woman can be a doctor |
| Putting a profession inside a gender | Not all doctors are women, so it is overlap, not inside |
| Mixing "class" and "property" | "Fruits" and "Red things" overlap (some fruits are red) |
| Male and female relations | Brothers and sisters are separate; both are inside "Siblings" |
| Forgetting the third pair | A diagram can fit two pairs and still fail the third |
| Counting "all three" twice | "A and B" in a survey usually includes those in all three |
Venn Diagram Questions for SSC CGL (Practice Set with Answers)
- Which diagram fits: Kerala, India, World? Answer: Three nested circles. Kerala ⊂ India ⊂ World.
- Teachers, Women, Trees? Answer: Teachers and Women overlap; Trees separate (type 11).
- Fish, Sharks, Birds? Answer: Sharks inside Fish; Birds separate (type 7).
- Singers, Dancers, Actors? Answer: Three circles all crossing (type 4).
- Brothers, Sisters, Siblings? Answer: Two separate circles inside one big circle (type 5).
- Nurses, Females, Mothers? Answer: Mothers inside Females; Nurses cross both (type 9). Some nurses are male, some mothers are nurses.
- In a group of 80 people, 45 read newspaper A, 38 read B and 15 read both. How many read neither? Answer: 12. 80 − (45 + 38 − 15).
- Of 70 students, 30 play cricket, 25 football and 20 hockey; 8 play cricket and football, 6 football and hockey, 7 cricket and hockey, and 3 play all three. How many play none? Answer: 13. At least one = 57.
- In question 8, how many play only cricket? Answer: 18. 30 − 8 − 7 + 3.
- In question 8, how many play exactly two games? Answer: 12. (8 + 6 + 7) − 3 × 3.
For timed practice, take the SSC CGL Reasoning Mini Mock Test 04 and the SSC CHSL Reasoning Mini Mock Test 01.
Venn Diagram Questions FAQs
What is a Venn diagram in reasoning?
It is a set of circles that shows how groups relate. A circle inside another means "all of one are the other"; crossing circles mean "some are"; separate circles mean "none are".
How do you solve logical Venn diagram questions fast?
Check the three pairs one at a time (inside, overlap or separate), start drawing from the largest group, and pick the only option that fits all three pairs.
What is the formula for a Venn diagram with 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).
How do you find "only A" in a three-circle Venn diagram?
Only A = n(A) − n(A∩B) − n(A∩C) + n(A∩B∩C), when the pair figures include those in all three.
How many Venn diagram questions come in SSC CGL?
Usually 1 question in SSC CGL Tier 1 reasoning, either a logical diagram or a region-counting figure. SSC CHSL, MTS, GD and RRB NTPC ask 1 to 2.
Is a Venn diagram the same as a syllogism?
They use the same logic. Syllogism gives statements like "Some A are B" and asks what follows; Venn diagram questions give word groups and ask which picture fits. Drawing Venn circles is the best way to solve syllogisms.
Practice Next
- Mock tests: SSC CGL Reasoning Mini Mock Test 03, SSC CGL Reasoning Mini Mock Test 04 and SSC CHSL Reasoning Mini Mock Test 02.
- Related notes: syllogism possibility rules, syllogism only a few rules, direction sense questions for SSC CGL and dice questions for SSC CGL.
- Exam details: SSC CGL 2026 and SSC CHSL 2026.
- Browse all study notes.