Venn Diagram for SSC MTS — Relationships Between Classes Made Simple

beginner 12 min read

Concept

A Venn diagram is a picture of how two or more groups (classes) relate to each other. Each group is represented by a circle. Where the circles sit relative to each other — inside, overlapping, or completely separate — tells you the relationship between those groups.

Here is the plain-language version: you are answering one question, "Can a member of Group A also be a member of Group B?" Depending on the answer, one of exactly three situations applies.

Situation 1 — One group is entirely inside the other. All dogs are animals, but not all animals are dogs. So the Dogs circle sits completely inside the Animals circle. This is called a subset or subclass relationship.

Situation 2 — The groups partially overlap. Some doctors are also singers. Not all doctors sing, and not all singers are doctors — but there is a middle zone where both descriptions fit the same person. The circles partially intersect.

Situation 3 — The groups have nothing in common. A chair cannot be a river. These two groups share zero members. The circles sit completely separate, no touching, no overlap.

Think of it like this analogy: imagine three rooms in a building. Room A and Room B have a shared corridor (partial overlap). Room C is a separate building entirely (no relation). And Room D is a tiny closet that sits entirely inside Room A (subset). Your job in the exam is to identify which arrangement the question is describing.

SSC MTS tests this in two ways. First, it gives you three classes and asks you to pick the correct diagram. Second, it gives you a diagram with numbered regions and asks which region represents a specific combination (e.g., "military officers who are short but not strong"). Both question types come down to the same three relationships above — once you internalize them, you are done.


Deep Dive

The Three Fundamental Relationships

Type 1: Subset (One Inside the Other)

This applies when every member of one class is necessarily a member of the other, but not vice versa.

Recognition trigger: the word "is a type of" or "is a kind of" signals subset. Ask yourself — can every X be a Y? If yes, X is inside Y.

Type 2: Partial Overlap (Intersecting Circles)

This applies when some members of Group A can also belong to Group B, but membership in one does not guarantee membership in the other.

Recognition trigger: the words "some," "can be," "may be." Ask yourself — is it possible for an X to be a Y? If yes, but not guaranteed, they overlap.

Type 3: No Relationship (Disjoint Circles)

This applies when it is impossible for a member of one class to belong to the other.

Recognition trigger: ask yourself — can any X ever be a Y? If the answer is a definitive no, the circles are separate.

Region Identification (The Second Question Type)

Look at a standard three-shape diagram: Circle (C), Square (S), Triangle (T), with overlapping regions labeled 1 through 7 (or fewer, depending on how many shapes overlap).

The logic is: a region that is inside Shape X but outside Shape Y means "belongs to X, does not belong to Y."

Work through conditions one by one:

A common exam setup uses exactly three shapes with seven distinct regions. Here is how to read any region:

| Inside | Outside | Meaning | |---|---|---| | Circle only | Square, Triangle | Belongs to C only | | Circle + Square | Triangle | Belongs to C and S, not T | | Circle + Square + Triangle | Nothing | Belongs to all three | | Square + Triangle | Circle | Belongs to S and T, not C |

The method: list the conditions, check each shape one by one, eliminate regions that fail any condition.

Common Class Pairs Tested in SSC MTS

Memorize these patterns — they appear repeatedly:

| Classes Given | Correct Relationship | |---|---| | Hockey, Cricket, Games | Hockey and Cricket are both inside Games (two separate circles inside a larger one) | | Sun, Planets, Jupiter | Jupiter inside Planets; Sun completely separate | | Painters, Lawyers, Singers | Three overlapping circles (professions can coexist) | | Men, Humans, Mammals | Concentric: Men inside Humans inside Mammals | | Doctors, Fathers, Sportsmen | Three overlapping circles (all three can coexist in one person) | | Oak, Mango, Trees | Oak and Mango are separate circles inside Trees |

The underlying logic for each: check if any class is a strict subset of another, then check if any two are mutually exclusive.

Step-by-Step Method for "Choose the Correct Diagram" Questions

  1. Take the three given classes. Label them A, B, C.
  2. Ask: Is A a type of B? Is B a type of A? If yes to either → subset relationship.
  3. Ask: Can any A be a B? If yes but not necessarily → overlap.
  4. Ask: Is it impossible for A to be B? If yes → disjoint circles.
  5. Repeat steps 2–4 for all three pairs: (A,B), (B,C), (A,C).
  6. Match to the answer option whose diagram matches all three pair-relationships simultaneously.

Memory Tricks & Shortcuts

eliminationThe Bucket Test

For any two classes, ask the Bucket Test: "Can I pour water from Bucket A into Bucket B?" If all of A fits into B → subset. If some of A fits → overlap. If none → disjoint. Apply this mentally to all three pairs in under 10 seconds. Standard method of drawing and comparing: 45 seconds. Bucket Test applied mentally: 10 seconds. That is a 35-second saving per question.

patternProfession Trap — Always Overlapping

Any question with three human professions or roles (doctor, singer, teacher; painter, lawyer, father; etc.) is always three overlapping circles. A single human can hold multiple professions simultaneously. You do not need to analyze these — the moment you see three human roles or occupations, pick "three mutually overlapping circles." Standard analysis: 30 seconds. Pattern recognition: 3 seconds.

patternSport/Game Subset Pattern

Any question pairing specific games (Hockey, Cricket, Football) with a parent category (Games, Sports, Indoor Games) follows the same pattern: the specific games are separate circles inside the parent circle. They do not overlap with each other because Cricket is not Hockey. Recognizing this pattern eliminates all wrong options in one step. Instead of 4 elimination checks (40 seconds), this takes 5 seconds.

eliminationRegion Counting — Inside-Outside Checklist

For region-identification questions, write the condition as a checklist: IN [shape1], IN [shape2], OUT [shape3]. Then physically trace each labeled region in the diagram. A region fails as soon as it violates one condition. Cross it out and move on. This systematic elimination prevents the most common error (picking a region that satisfies two conditions but fails the third). Takes 15 steps instead of guessing and rechecking (which can take 60+ seconds on a complex diagram).

eliminationThe Celestial Bodies Trap

Questions involving Sun, Moon, Planets, Stars, Earth almost always test whether you know that Sun is a star (not a planet) and Moon is a satellite (not a planet). This makes them disjoint from the Planets category. Earth and Jupiter are inside Planets, but Sun/Moon are outside. Recognizing this instantly eliminates three wrong options without any diagram analysis. Standard analysis: 25 seconds. Factual recall: 4 seconds.


Fast-Solving Framework

In the exam hall, follow this decision tree for every Venn diagram question:

Question type 1: "Choose the correct diagram for these three classes"

Step 1 — Scan for the profession pattern: three human roles? → Three overlapping circles. Done.

Step 2 — Scan for the game/sport pattern: specific type + parent category? → Types are separate circles inside the parent. Done.

Step 3 — If neither pattern applies, run the Bucket Test on all three pairs. Note: subset / overlap / disjoint for each pair. Match to the answer option.

Step 4 — If two options look similar, check the one pair that differs between them.

Question type 2: "Which region represents [condition]?"

Step 1 — Convert the condition into a checklist: inside which shapes, outside which shapes.

Step 2 — Start with the most restrictive condition (usually "NOT in" a shape). Eliminate all regions inside that shape immediately.

Step 3 — From surviving regions, find the one satisfying all remaining "inside" conditions.

Step 4 — That is your answer. Do not second-guess it.

Target time per question: 15–20 seconds for Type 1, 20–30 seconds for Type 2.


Solved PYQs

Why this question: This is the foundational "three professions" question type. Getting this right confirms you understand the partial-overlap principle.

Previous Year Questionपिछले वर्ष का प्रश्न2019
Identify the Venn diagram that best represents the relationship between the given classes. Painter, Lawyer, Singer
  1. Two separate circles
  2. Two circles where one overlaps partially with another
  3. Three overlapping circles
  4. Three circles where all three overlap
Solutionसमाधान
A painter can also be a singer and/or a lawyer; the three professions can overlap. The best representation uses three overlapping circles, as a person can belong to any combination of these categories.

Solving path: Apply the Profession Trap shortcut. Painter, Lawyer, Singer are three human professions. Can one person be all three? Yes — a person can paint, practice law, and sing. Can any two coexist? Yes. Are any two mutually exclusive? No. Therefore all three circles must overlap with each other. The answer is three overlapping circles. Time taken: 5 seconds.


Why this question: This is the classic region-identification question. It tests whether you can read a labeled diagram and isolate the correct region.

Previous Year Questionपिछले वर्ष का प्रश्न2013
In the given diagram, Circle represents strong men, Square represents short men and Triangle represents military officers. Which region represents military officers who are short but not strong?
  1. 2
  2. 4
  3. 3
  4. 1
Solutionसमाधान
Region 2 lies inside both the Triangle (military officers) and the Square (short men) but outside the Circle (strong men), representing military officers who are short but not strong.

Solving path: Write the condition as a checklist: IN Triangle (military officer), IN Square (short), OUT Circle (not strong). Region 2 lies inside both Triangle and Square but outside Circle. Check: does it satisfy all three? Triangle — yes. Square — yes. Circle — outside, so "not strong" — yes. Region 2 is correct. Time taken: 20 seconds using the checklist method.


Why this question: This tests the Game/Sport subset pattern — a very frequent SSC MTS setup.

Previous Year Questionपिछले वर्ष का प्रश्न2017
Choose the correct Venn diagram which best illustrates the relationship among Hockey, Cricket, Games.
  1. (b) Two circles inside a larger circle
  2. (d) Two circles inside a square
  3. (a) Two overlapping circles inside a rectangle
  4. (c) Two overlapping circles inside a larger one
Solutionसमाधान
Both Hockey and Cricket are types of Games, so both should be inside the Games circle. Hockey and Cricket are different games with no overlap, so they appear as two separate circles within the Games circle.

Solving path: Hockey and Cricket are both types of Games. Apply the Bucket Test: Does Hockey fit inside Games? Yes. Does Cricket fit inside Games? Yes. Are Hockey and Cricket the same thing? No — they are separate, non-overlapping sports. Result: two separate circles inside the Games circle. Answer: option (b). Time taken: 8 seconds.


Why this question: A repeat of the three-professions type from a different year — confirms the pattern is a consistent SSC MTS favorite.

Previous Year Questionपिछले वर्ष का प्रश्न2019
Identify the Venn diagram that best represents the relationship between the given classes: Painter, Lawyer, Singer
  1. (b) Two overlapping circles with one inside
  2. (c) Two separate circles
  3. (a) Three mutually overlapping circles
  4. (d) Three circles in a chain overlap
Solutionसमाधान
Painters, Lawyers, and Singers are three different professions that can partially overlap — some people can be both painters and singers, both singers and lawyers, etc. — so three mutually intersecting circles best represent this relationship.

Solving path: Same three professions as the first question. Profession Trap applies directly. A single person can be Painter + Lawyer + Singer simultaneously. No two professions are mutually exclusive. Answer is three mutually overlapping circles — option (a). Time taken: 4 seconds, pattern recognition only.


Why this question: Tests the Celestial Bodies Trap — mixing a star, a category, and a specific planet.

Previous Year Questionपिछले वर्ष का प्रश्न2020
Select the Venn diagram that best illustrates the relationship among the following classes: Sun, Planets, Jupiter
  1. (d) Two separate circles with one below
  2. (b) Three concentric circles
  3. (c) Two circles with one inside
  4. (a) Two separate circles with one inside another
Solutionसमाधान
Jupiter is a planet so it should be inside the Planets circle. The Sun is a star and not a planet, so it should be represented as a completely separate circle outside the Planets circle.

Solving path: Jupiter is a planet — Jupiter goes inside the Planets circle. The Sun is a star, not a planet — Sun's circle is completely outside Planets. Now check: is the Sun related to Jupiter directly? No special relationship beyond both being in the solar system — they do not share a class membership. Result: Planets circle contains Jupiter; Sun is a separate circle entirely outside Planets. This matches option (a): two separate circles with one inside another (Jupiter inside Planets, Sun outside). Time taken: 10 seconds.


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