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Syllogisms Questions for Placement Exams

Last Updated: March 2026

Introduction to Syllogisms

Syllogisms is a logical reasoning topic that tests your ability to draw conclusions from given statements using deductive logic. This topic is essential for placement exams at companies like TCS, Infosys, Wipro, Cognizant, Deloitte, KPMG, and banking sector, as well as sarkari exams including SSC CGL, Bank PO (SBI, IBPS), Railway, and UPSC CSAT.

Why Syllogisms is Important:

  • Tests pure logical deduction skills
  • No calculations required - only reasoning
  • Frequently asked in reasoning sections (5-8 questions)
  • Foundation for critical thinking and argument analysis
  • High accuracy potential with proper technique

Important Concepts and Rules

Basic Structure

A syllogism consists of:

  • Two Premises (Statements): Given facts/propositions
  • One Conclusion: Derived from the premises

Standard Forms

FormStatement PatternExample
Universal Affirmative (A)All A are BAll cats are mammals
Universal Negative (E)No A is BNo cat is a dog
Particular Affirmative (I)Some A are BSome cats are black
Particular Negative (O)Some A are not BSome cats are not pets

Syllogism Rules (Venn Diagram Method)

Rule 1: All A are B

  • Circle A is completely inside circle B
  • Conclusion possibilities:
    • Some A are B ✓
    • Some B are A ✓
    • All B are A ✗ (not necessarily)

Rule 2: No A is B

  • Circles A and B do not overlap at all
  • Conclusion possibilities:
    • No B is A ✓ (same statement)
    • Some A are not B ✓
    • Some B are not A ✓

Rule 3: Some A are B

  • Circles A and B overlap partially
  • Conclusion possibilities:
    • Some B are A ✓
    • All A are B ✗
    • No A is B ✗

Rule 4: Some A are not B

  • Part of circle A is outside circle B
  • Conclusion possibilities:
    • Some A are B ✗ (not certain)
    • All A are B ✗

Shortcut Rules (For Quick Solving)

Statement 1Statement 2Valid Conclusion
All A are BAll B are CAll A are C ✓
All A are BSome B are CSome A are C? Not necessarily
Some A are BAll B are CSome A are C ✓
No A is BAll B are CSome C are not A ✓
All A are BNo B is CNo A is C ✓

Complementary Pairs (Either/Or Cases)

When both conclusions seem false individually but cover all possibilities:

  • Some A are B + No A is B → Either follows
  • Some A are not B + All A are B → Either follows

Common Mistakes to Avoid

  1. Assuming Categories: "All A are B" doesn't mean "All B are A"
  2. Existential Fallacy: Don't assume existence from universal statements
  3. Illicit Minor/Major: Middle term must be distributed properly
  4. Some ≠ All: "Some" means at least one, possibly all

Practice Questions

Level 1: Easy

Question 1: Basic All-Some Relationship Statements:

  1. All roses are flowers.
  2. All flowers are plants.

Conclusions: I. All roses are plants. II. Some plants are roses.

<details> <summary>Solution</summary>

Venn Diagram: Roses ⊂ Flowers ⊂ Plants

I. All roses are plants: Since roses ⊂ flowers and flowers ⊂ plants, roses ⊂ plants. ✓ TRUE

II. Some plants are roses: Since all roses are plants, at least those roses are plants. ✓ TRUE

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Question 2: No Relationship Statements:

  1. No table is a chair.
  2. No chair is a sofa.

Conclusions: I. No table is a sofa. II. Some sofas are not chairs.

<details> <summary>Solution</summary>

I. No table is a sofa: Tables and sofas could still overlap (both different from chairs). Not necessarily true. ✗

II. Some sofas are not chairs: From "No chair is a sofa", all sofas are not chairs (since no overlap). So definitely some sofas are not chairs. ✓ TRUE

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Question 3: Some Relationship Statements:

  1. Some cats are dogs.
  2. All dogs are animals.

Conclusions: I. Some cats are animals. II. All cats are animals.

<details> <summary>Solution</summary>

Venn: Cats and Dogs overlap, Dogs ⊂ Animals So part of Cats (that overlaps with Dogs) is inside Animals.

I. Some cats are animals: The cats that are dogs are animals. ✓ TRUE

II. All cats are animals: Only some cats (those that are dogs) are necessarily animals. ✗

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Question 4: Direct Conclusion Statements:

  1. All books are pages.
  2. Some pages are words.

Conclusions: I. Some books are words. II. Some words are pages.

<details> <summary>Solution</summary>

I. Some books are words: Books ⊂ Pages, and Some Pages are Words. Books may or may not overlap with Words. ✗

II. Some words are pages: Directly from statement 2. ✓ TRUE

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Question 5: Negative Conclusion Statements:

  1. All pens are inks.
  2. No ink is a pencil.

Conclusions: I. No pen is a pencil. II. Some pencils are not inks.

<details> <summary>Solution</summary>

Venn: Pens ⊂ Inks, Inks ∩ Pencils = ∅ So Pens ∩ Pencils = ∅

I. No pen is a pencil: Since pens ⊂ inks and inks ∩ pencils = ∅. ✓ TRUE

II. Some pencils are not inks: From "No ink is a pencil", pencils and inks don't overlap, so all pencils are not inks, which means some pencils are not inks. ✓ TRUE

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Question 6: Some-All Chain Statements:

  1. Some A are B.
  2. All B are C.

Conclusions: I. Some A are C. II. Some C are A.

<details> <summary>Solution</summary>

Venn: A overlaps B, B ⊂ C So A overlaps C (through B).

I. Some A are C: The A that are B are also C. ✓ TRUE

II. Some C are A: Same as I (just reversed). ✓ TRUE

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Question 7: Complex Premises Statements:

  1. All men are humans.
  2. Some humans are doctors.
  3. All doctors are professionals.

Conclusions: I. Some humans are professionals. II. Some professionals are men.

<details> <summary>Solution</summary>

From 2 and 3: Some humans are doctors, and all doctors are professionals. So some humans are professionals. ✓ I follows

For II: Men ⊂ Humans. Some humans are professionals. The overlap could be entirely outside men. Not necessarily true. ✗

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Question 8: No-All Combination Statements:

  1. No fruit is a vegetable.
  2. All carrots are vegetables.

Conclusions: I. No carrot is a fruit. II. Some vegetables are not fruits.

<details> <summary>Solution</summary>

Venn: Fruits ∩ Vegetables = ∅, Carrots ⊂ Vegetables

I. No carrot is a fruit: Carrots ⊂ Vegetables, and Vegetables ∩ Fruits = ∅. So Carrots ∩ Fruits = ∅. ✓ TRUE

II. Some vegetables are not fruits: Since carrots are vegetables and no carrot is a fruit, at least carrots are vegetables that are not fruits. ✓ TRUE

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Question 9: Identical Conclusions Statements:

  1. All squares are rectangles.
  2. All rectangles are parallelograms.

Conclusions: I. All squares are parallelograms. II. All parallelograms are squares.

<details> <summary>Solution</summary>

I. All squares are parallelograms: Squares ⊂ Rectangles ⊂ Parallelograms. ✓ TRUE

II. All parallelograms are squares: Reverse doesn't follow. Parallelograms include rectangles, rhombuses, etc. ✗

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Question 10: Particular Premises Statements:

  1. Some birds can fly.
  2. Some flying creatures are insects.

Conclusions: I. Some birds are insects. II. Some insects can fly.

<details> <summary>Solution</summary>

I. Some birds are insects: The overlap between birds and flying creatures, and flying creatures and insects, doesn't guarantee birds and insects overlap. ✗

II. Some insects can fly: Directly from statement 2 (rephrased). ✓ TRUE

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Level 2: Medium

Question 11: Three-Statement Syllogism Statements:

  1. All rivers are water bodies.
  2. Some water bodies are lakes.
  3. All lakes are freshwater.

Conclusions: I. Some water bodies are freshwater. II. Some rivers are lakes.

<details> <summary>Solution</summary>

From 2 and 3: Some water bodies (those that are lakes) are freshwater. ✓ I follows

For II: Rivers ⊂ Water bodies, Some water bodies are lakes. Rivers may or may not be among those water bodies that are lakes. ✗

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Question 12: Distributed Middle Statements:

  1. All teachers are educated.
  2. Some educated people are employed.

Conclusions: I. Some teachers are employed. II. Some employed people are educated.

<details> <summary>Solution</summary>

I. Some teachers are employed: Teachers ⊂ Educated, Some Educated are Employed. Teachers may or may not overlap with employed. ✗

II. Some employed people are educated: Direct from statement 2. ✓ TRUE

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Question 13: Complementary Case Setup Statements:

  1. Some students are intelligent.
  2. All intelligent people are hardworking.

Conclusions: I. Some students are hardworking. II. No student is hardworking.

<details> <summary>Solution</summary>

I. Some students are intelligent and all intelligent are hardworking → Some students are hardworking. ✓ TRUE

II. No student is hardworking: Contradicts I. ✗

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Question 14: Neither-Nor Case Statements:

  1. Some A are B.
  2. No B is C.

Conclusions: I. Some A are not C. II. No A is C.

<details> <summary>Solution</summary>

Venn: A overlaps B, B ∩ C = ∅ So the A that are B are definitely not C.

I. Some A are not C: The A that are B are not C. ✓ TRUE

II. No A is C: Only those A that are B are not C. Other A could be C. ✗

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Question 15: Possible Conclusions Statements:

  1. All lions are wild animals.
  2. Some wild animals are carnivores.

Conclusions: I. Some lions are carnivores. II. All carnivores are wild animals.

<details> <summary>Solution</summary>

I. Some lions are carnivores: Lions ⊂ Wild animals, Some wild animals are carnivores. Lions may or may not be among those wild animals. ✗ (possible but not definite)

II. All carnivores are wild animals: Only some wild animals are carnivores, not all. ✗

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Question 16: Reverse Relationship Statements:

  1. All mobile phones are electronic devices.
  2. Some electronic devices are expensive.

Conclusions: I. Some expensive things are mobile phones. II. Some mobile phones are expensive.

<details> <summary>Solution</summary>

Venn: Mobiles ⊂ Electronics, Electronics overlaps Expensive

I. Some expensive things are mobile phones: The overlap of Electronics and Expensive may not include Mobiles. ✗

II. Some mobile phones are expensive: Same reasoning - not necessarily true. ✗

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Question 17: Definite-Negative Chain Statements:

  1. No circle is a square.
  2. All squares are rectangles.

Conclusions: I. No rectangle is a circle. II. Some rectangles are not circles.

<details> <summary>Solution</summary>

Venn: Circles ∩ Squares = ∅, Squares ⊂ Rectangles

I. No rectangle is a circle: Rectangles include squares (not circles) and possibly others. Other rectangles could be circles. ✗

II. Some rectangles are not circles: Squares are rectangles and not circles. ✓ TRUE

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Question 18: All-Some-Not Combination Statements:

  1. All managers are employees.
  2. Some employees are not supervisors.

Conclusions: I. Some managers are not supervisors. II. No manager is a supervisor.

<details> <summary>Solution</summary>

Managers ⊂ Employees. Some employees are not supervisors. The "not supervisors" could all be non-managers.

I. Some managers are not supervisors: Not definite - the overlap could be outside managers. ✗

II. No manager is a supervisor: Even stronger, definitely doesn't follow. ✗

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Question 19: Complete Mediate Inference Statements:

  1. All dogs are mammals.
  2. All mammals are animals.
  3. Some animals are pets.

Conclusions: I. All dogs are animals. II. Some dogs are pets.

<details> <summary>Solution</summary>

I. All dogs are animals: Dogs ⊂ Mammals ⊂ Animals. ✓ TRUE

II. Some dogs are pets: Dogs ⊂ Animals, Some Animals are Pets. Dogs may or may not overlap with pets. ✗

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Question 20: Either-Or Case Identification Statements:

  1. Some students are toppers.
  2. All toppers are brilliant.

Conclusions: I. Some students are brilliant. II. No student is brilliant.

<details> <summary>Solution</summary>

I. Some students are toppers, all toppers are brilliant → Some students are brilliant. ✓ TRUE

II. No student is brilliant: Definitely false (contradicts I).

Since I is definitely true: Answer: Only I follows

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Level 3: Hard

Question 21: Multi-Level Deduction Statements:

  1. All athletes are sportspersons.
  2. Some sportspersons are winners.
  3. No winner is a loser.
  4. Some losers are athletes.

Conclusions: I. Some sportspersons are not losers. II. Some athletes are not losers.

<details> <summary>Solution</summary>

From 1 and 4: All athletes are sportspersons, some losers are athletes. So some losers are sportspersons (those that are athletes).

From 2 and 3: Some sportspersons are winners, no winner is a loser. So those sportspersons who are winners are not losers. Therefore, some sportspersons are not losers. ✓ I follows

For II: Some losers are athletes (statement 4). This means some athletes are losers. But we can't conclude that some athletes are NOT losers from this alone. Actually, since some athletes are losers, "some athletes are not losers" might seem separate, but...

Wait - statement 4 says some losers are athletes, meaning there's overlap. Statement 3 says no winner is a loser. Statement 1 says all athletes are sportspersons.

Can we prove some athletes are not losers? Consider: Athletes who are winners (from statement 2, some sportspersons are winners, and athletes are sportspersons, so possibly some athletes are winners). Those athletes who are winners are not losers (from 3). So some athletes (the winners among them) are not losers. ✓ II follows

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Question 22: Complex Distribution Statements:

  1. All A are B.
  2. Some B are C.
  3. All C are D.
  4. No D is E.

Conclusions: I. Some B are not E. II. Some A are D.

<details> <summary>Solution</summary>

From 3 and 4: All C are D, No D is E → No C is E. From 2: Some B are C. Since no C is E, those B that are C are not E. So some B are not E. ✓ I follows

For II: All A are B, Some B are C, All C are D. The chain doesn't guarantee A overlaps with C. A may be entirely within B but outside the "some B that are C". So we can't say some A are D. ✗

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Question 23: Negative-Positive Mix Statements:

  1. No metal is a gas.
  2. All liquids are gases.
  3. Some liquids are compounds.

Conclusions: I. No compound is a metal. II. Some compounds are not metals.

<details> <summary>Solution</summary>

From 1 and 2: No metal is gas, all liquids are gases → No liquid is metal. From 3: Some liquids are compounds. Since no liquid is metal, and some liquids are compounds: Those compounds that are liquids are not metals. So some compounds are not metals. ✓ II follows

For I: Only some compounds (those that are liquids) are not metals. Other compounds could be metals. So "no compound is metal" is too strong. ✗

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Question 24: Possibility Analysis Statements:

  1. Some managers are leaders.
  2. All leaders are decision-makers.
  3. Some decision-makers are not effective.

Conclusions: I. Some managers are effective. II. Some leaders are not effective.

<details> <summary>Solution</summary>

I. Some managers are effective: Managers overlap Leaders, Leaders ⊂ Decision-makers, Some Decision-makers are not effective. The "not effective" decision-makers might not include any managers/leaders. Not necessarily true. ✗

II. Some leaders are not effective: Leaders ⊂ Decision-makers. Some decision-makers are not effective. These could be entirely outside leaders. Not necessarily true. ✗

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Question 25: Complete Analysis Required Statements:

  1. All triangles are polygons.
  2. Some polygons are regular.
  3. All regular shapes are symmetric.
  4. No polygon is a circle.

Conclusions: I. Some triangles are symmetric. II. No triangle is a circle.

<details> <summary>Solution</summary>

I. Some triangles are symmetric: Triangles ⊂ Polygons, Some polygons are regular, All regular are symmetric. The "some regular polygons" may not include any triangles. Not necessarily true. ✗

II. No triangle is a circle: Triangles ⊂ Polygons, No polygon is a circle → No triangle is a circle. ✓ TRUE

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Question 26: Categorical Complex Statements:

  1. Some doctors are surgeons.
  2. All surgeons are specialists.
  3. No specialist is a general practitioner.
  4. Some general practitioners are physicians.

Conclusions: I. Some doctors are not general practitioners. II. No surgeon is a general practitioner.

<details> <summary>Solution</summary>

From 2 and 3: All surgeons are specialists, no specialist is GP → No surgeon is GP. ✓ II follows

For I: Some doctors are surgeons, no surgeon is GP. Those doctors who are surgeons are not GPs. So some doctors are not general practitioners. ✓ I follows

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Question 27: Indirect Relationship Statements:

  1. All trains are vehicles.
  2. Some vehicles are public transport.
  3. All public transport is subsidized.
  4. No car is a train.

Conclusions: I. Some vehicles are subsidized. II. No car is a vehicle.

<details> <summary>Solution</summary>

From 2 and 3: Some vehicles are public transport, all public transport is subsidized → Some vehicles are subsidized. ✓ I follows

From 1: All trains are vehicles. From 4: No car is a train. Cars could still be vehicles (non-train vehicles). ✗ II doesn't follow

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Question 28: Distributive Fallacy Check Statements:

  1. All A are B.
  2. All C are B.

Conclusions: I. Some A are C. II. Some B are A.

<details> <summary>Solution</summary>

A and C could be completely separate subsets of B (no overlap).

I. Some A are C: Not necessarily true. ✗

II. Some B are A: Since all A are B, at least those A are B. ✓ TRUE

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Question 29: Existential Import Statements:

  1. All unicorns are mythical creatures.
  2. All mythical creatures are fictional.

Conclusions: I. All unicorns are fictional. II. Some mythical creatures are unicorns.

<details> <summary>Solution</summary>

I. All unicorns are fictional: Unicorns ⊂ Mythical ⊂ Fictional. ✓ TRUE

II. Some mythical creatures are unicorns: From "All unicorns are mythical", we can infer "Some mythical are unicorns" only if unicorns exist. In traditional logic with existential import, this follows. ✓ TRUE

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Question 30: Complete Integration Statements:

  1. All P are Q.
  2. Some Q are R.
  3. All R are S.
  4. Some S are not T.
  5. All T are U.

Conclusions: I. Some Q are S. II. Some P are not T.

<details> <summary>Solution</summary>

From 2 and 3: Some Q are R, all R are S → Some Q are S. ✓ I follows

For II: All P are Q. Some Q are S. Some S are not T. The chain P→Q→S→not T may not connect. P could be entirely within the part of Q that's not R, or within R but R might be entirely within S that's T. Actually some S are not T, but some S might be T (those related to U). Cannot definitively say some P are not T. ✗

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Companies & Exams Asking Syllogisms

Top Companies

  • TCS, Infosys, Wipro, Cognizant - 2-3 questions, moderate
  • Deloitte, KPMG, EY - Logical reasoning focus, medium-hard
  • Banking Sector (SBI, IBPS, RBI) - 5-10 questions, high weightage
  • Consulting Firms - Complex multi-statement sets

Government Exams

  • SBI PO/Clerk, IBPS PO/Clerk - Heavy focus, 5-10 questions
  • SSC CGL/CHSL - 2-4 questions, moderate
  • RBI Grade B, NABARD - Advanced syllogisms
  • Insurance (LIC, NIACL, GIC) - Similar to banking
  • UPSC CSAT - Mixed with other reasoning

Preparation Tips

  1. Master Venn Diagrams: Always draw Venn diagrams for complex statements. Visual representation prevents errors.

  2. Remember the Basics:

    • "All A are B" ≠ "All B are A"
    • "Some A are B" = "Some B are A"
    • "No A is B" = "No B is A"

  3. Check Each Conclusion Independently: Don't carry over assumptions from one conclusion to another.

  4. Watch for Complementary Pairs: When conclusions seem contradictory but cover all possibilities, answer might be "either follows."

  5. Avoid Real-World Assumptions: Stick strictly to the given statements. Don't use outside knowledge.

  6. Practice Standard Patterns: Most syllogisms follow predictable patterns. Recognize them quickly.

  7. Use Elimination: In multiple choice, eliminate clearly wrong options first.

Frequently Asked Questions (FAQs)

Q1: What's the fastest way to solve syllogisms?

Use Venn diagrams for complex problems. For simpler ones, apply the direct rules:

  • All + All = All
  • All + Some = No definite conclusion
  • Some + All = Some
  • No + All = Some not

Q2: When is the answer "Either I or II follows"?

When both conclusions cannot be true together, but one must be true, and both are individually possible (I is not definitely true, II is not definitely true, but I or II must be true).

Q3: Can I use the rules without drawing Venn diagrams?

For simple 2-statement syllogisms, yes. But for 3+ statements or complex relationships, Venn diagrams are safer and often faster than mental calculation.

Q4: What does "Some" mean exactly in syllogisms?

"Some" means "at least one and possibly all." It indicates an overlap between categories, but doesn't specify how much overlap.

Q5: Are syllogism questions getting harder in recent exams?

Recent trends show more "possibility" questions and combined syllogism-data interpretation sets. Multi-statement problems (4-5 premises) are also becoming more common.

Master syllogisms with Venn diagrams and rule-based practice!

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