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Basic Two-Statement Syllogism

Introduction

Basic Two-Statement Syllogism என்பது aptitude exams-இல் வரும் logical reasoning கேள்விகளின் அடிப்படை. இதில் இரண்டு factual statements கொடுக்கப்பட்டு, அவற்றிலிருந்து எந்த conclusion(s) logic-ஆக follow ஆகிறது என்பதை தீர்மானிக்க வேண்டும்.

இந்த pattern-ஐ புரிந்துகொள்வது, direct logical relations-ஐ Venn diagrams அல்லது conceptual reasoning பயன்படுத்தி மதிப்பீடு செய்யும் திறனை வளர்க்கிறது.

Pattern: Basic Two-Statement Syllogism

Pattern

முக்கிய கருத்து: “All”, “Some”, “No” போன்ற statements-ஐ பயன்படுத்தி, இரண்டு categories-க்கிடையிலான direct அல்லது transitive relations-ஐ சோதிப்பது.

பொதுவாக இரண்டு statements மற்றும் இரண்டு அல்லது அதற்கு மேற்பட்ட conclusions கொடுக்கப்படும். அந்த conclusions-ல் எவை definitely follow ஆகின்றன என்பதை நீங்கள் தீர்மானிக்க வேண்டும்.

Step-by-Step Example

Question

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

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

Options:
A. Only Conclusion I follows
B. Only Conclusion II follows
C. Either I or II follows
D. Neither I nor II follows

Solution

  1. Step 1: Relationship-ஐ visualize செய்தல்

    “All cats are animals” → Cats circle முழுவதும் Animals circle-க்குள் இருக்கும்.
    “Some animals are dogs” → Dogs circle, Animals-உடன் பகுதியளவில் overlap ஆகும்; Cats-உடன் overlap ஆக வேண்டும் என்பது அவசியமில்லை.

  2. Step 2: Conclusion I-ஐ சோதித்தல்

    “Some cats are dogs” → Cats மற்றும் Dogs இடையே நேரடி overlap கொடுக்கப்படவில்லை; ஆகவே இது அவசியமாக true அல்ல. ❌

  3. Step 3: Conclusion II-ஐ சோதித்தல்

    “All dogs are animals” → “Some animals are dogs” என்பதிலிருந்து இதை முடிவு செய்ய முடியாது; அது சில overlap இருப்பதை மட்டும் கூறுகிறது, முழுமையான inclusion அல்ல. ❌

  4. Final Answer:

    Neither I nor II follows. → Option D

  5. Quick Check:

    “Some animals are dogs” ≠ “All dogs are animals.”
    Cats மற்றும் Dogs இடையே definite connection இல்லை. எனவே இரண்டு conclusions-உம் invalid. ✅

Quick Variations

1. இரண்டு statements-உம் “All” கொண்டு தொடங்கலாம் (transitive logic).

2. ஒரு statement “Some” பயன்படுத்தி partial overlap-ஐ காட்டலாம்.

3. “All-Some” அல்லது “Some-All” mix, conclusions-ன் validity-ஐ மாற்றும்.

4. சில நேரங்களில், ஒரு positive மற்றும் ஒரு negative conclusion கொடுக்கப்பட்டால் “Either-Or” logic சோதிக்கப்படும்.

Trick to Always Use

  • Relationships-ஐ விரைவாக புரிந்துகொள்ள மூன்று circles (A, B, C) வரையுங்கள்.
  • “All + All” என்றால் transitive rule apply ஆகும் (All A are C).
  • “All + Some” என்றால் universal (“All”) conclusion எதுவும் follow ஆகாது.
  • Real-world facts-ஐ assume செய்யாதீர்கள் - கொடுக்கப்பட்ட statements-ல் உள்ள logic மட்டும் பயன்படுத்துங்கள்.

Summary

Summary

  • Statement types - “All”, “Some”, “No” - மற்றும் அவற்றின் direction-ஐ சரிபார்க்கவும்.
  • Logical follow-through முடிவு செய்வதற்கு முன் Venn diagrams பயன்படுத்துங்கள்.
  • “All + All” transitive logic-ஐ அனுமதிக்கும்; “All + Some” conclusions-ஐ கட்டுப்படுத்தும்.
  • General knowledge பயன்படுத்த வேண்டாம்; கொடுக்கப்பட்ட statements-ன் logic மட்டுமே கணக்கில் எடுத்துக்கொள்ள வேண்டும்.

நினைவில் வைக்க உதவும் example:
All A are B; All B are C ⇒ All A are C ✅

Practice

(1/5)
1. Statements: 1️⃣ All birds are animals. 2️⃣ Some animals are reptiles. Conclusions: I. Some birds are reptiles. II. All reptiles are animals.
easy
A. Only Conclusion I follows
B. Only Conclusion II follows
C. Both I and II follow
D. Neither I nor II follows

Solution

  1. Step 1: Visualize sets

    ‘All birds are animals’ ⇒ Birds fully inside Animals. ‘Some animals are reptiles’ ⇒ Reptiles partly overlap with Animals, but their exact position relative to Birds is unknown.

  2. Step 2: Test Conclusion I

    ‘Some birds are reptiles’ ⇒ Not necessarily true, as no direct overlap between Birds and Reptiles is established. ❌

  3. Step 3: Test Conclusion II

    ‘All reptiles are animals’ ⇒ Not proven, since ‘Some animals are reptiles’ only shows partial overlap, not total inclusion. ❌

  4. Final Answer:

    Neither Conclusion I nor II follows. → Option D

  5. Quick Check:

    Both statements show only partial and one-directional information; no definitive overlap or full inclusion between Birds and Reptiles. Hence, neither conclusion follows. ✅
Hint: ‘All + Some’ → Never assume total inclusion or guaranteed overlap.
Common Mistakes: Treating 'Some animals are reptiles' as 'All reptiles are animals'.
2. Statements: 1️⃣ All apples are fruits. 2️⃣ All fruits are sweet. Conclusions: I. All apples are sweet. II. Some sweet things are fruits.
easy
A. Only Conclusion I follows
B. Only Conclusion II follows
C. Both I and II follow
D. Neither I nor II follows

Solution

  1. Step 1: Establish relations

    ‘All apples are fruits’; ‘All fruits are sweet.’

  2. Step 2: Transitive logic

    If all apples are fruits and all fruits are sweet ⇒ All apples are sweet. ✅

  3. Step 3: Partial inclusion

    ‘All fruits are sweet’ implies ‘Some sweet things are fruits.’ ✅

  4. Final Answer:

    Both I and II follow. → Option C

  5. Quick Check:

    Apples ⊂ Fruits ⊂ Sweet ⇒ both conclusions logically hold. ✅
Hint: ‘All + All’ ⇒ Both direct and partial conclusions are valid.
Common Mistakes: Missing that ‘All’ implies ‘Some’.
3. Statements: 1️⃣ Some pens are pencils. 2️⃣ All pencils are stationery. Conclusions: I. Some stationery are pens. II. All pens are stationery.
easy
A. Only Conclusion I follows
B. Only Conclusion II follows
C. Both I and II follow
D. Neither I nor II follows

Solution

  1. Step 1: Interpret statements

    ‘Some pens are pencils’; ‘All pencils are stationery.’

  2. Step 2: Link the chain

    Those pens which are pencils are definitely stationery ⇒ Some stationery are pens. ✅

  3. Step 3: Test universal relation

    ‘All pens are stationery’ is not given, so cannot conclude. ❌

  4. Final Answer:

    Only Conclusion I follows. → Option A

  5. Quick Check:

    Partial overlap confirmed between pens and stationery. ✅
Hint: If ‘Some A are B’ and ‘All B are C’ ⇒ ‘Some C are A’.
Common Mistakes: Assuming all A are C from partial premise.
4. Statements: 1️⃣ All doctors are professionals. 2️⃣ Some professionals are teachers. Conclusions: I. Some teachers are doctors. II. Some professionals are doctors.
medium
A. Only Conclusion I follows
B. Only Conclusion II follows
C. Both I and II follow
D. Neither I nor II follows

Solution

  1. Step 1: Visualize relationship

    Doctors ⊂ Professionals; Some Professionals ↔ Teachers.

  2. Step 2: Check Conclusion I

    ‘Some teachers are doctors’ → No direct link, not valid. ❌

  3. Step 3: Check Conclusion II

    ‘Some professionals are doctors’ → True because all doctors are professionals, so at least some professionals are doctors. ✅

  4. Final Answer:

    Only Conclusion II follows. → Option B

  5. Quick Check:

    Doctors inside professionals; hence some professionals are definitely doctors. ✅
Hint: ‘All A are B’ ensures ‘Some B are A’.
Common Mistakes: Linking Teachers and Doctors without direct relation.
5. Statements: 1️⃣ All engineers are graduates. 2️⃣ Some graduates are artists. Conclusions: I. Some engineers are artists. II. Some artists are graduates.
medium
A. Only Conclusion I follows
B. Only Conclusion II follows
C. Both I and II follow
D. Neither I nor II follows

Solution

  1. Step 1: Identify relations

    ‘All engineers are graduates’; ‘Some graduates are artists.’

  2. Step 2: Test Conclusion I

    ‘Some engineers are artists’ → No link between engineers and artists. ❌

  3. Step 3: Test Conclusion II

    ‘Some artists are graduates’ → True by reversing the second statement. ✅

  4. Final Answer:

    Only Conclusion II follows. → Option B

  5. Quick Check:

    Artists ↔ Graduates confirmed; Engineers separate from artists. ✅
Hint: ‘Some A are B’ ⇒ ‘Some B are A’ is always true.
Common Mistakes: Assuming Engineers connect to Artists through Graduates.

Mock Test

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