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Three-Statement Chain Syllogism

Introduction

Three-Statement Chain Syllogism என்பது, இரண்டு-statement format-ஐத் தாண்டி, மற்ற இரண்டு sets-ஐ இணைக்கும் ஒரு intermediate term-ஐ அறிமுகப்படுத்துகிறது. இந்த pattern, logical chains of relationships ஐ அடையாளம் காணவும், பல premises-இலிருந்து செல்லுபடியாகும் transitive conclusions-ஐ உருவாக்கவும் உங்களைப் பயிற்சி செய்கிறது.

இது reasoning tests-ல் மிகவும் பொதுவான வகை, குறிப்பாக banking, SSC, மற்றும் CAT exams-ல், இரண்டு extreme terms இடையே இறுதி relation-ஐ candidates கண்டறிய வேண்டிய இடங்களில் அதிகம் கேட்கப்படுகிறது.

Pattern: Three-Statement Chain Syllogism

Pattern

The key concept: இரண்டு statements-க்கு ஒரு common middle term இருந்தால், direction மற்றும் type அனுமதிக்கும் பட்சத்தில், முதல் term மற்றும் கடைசி term இடையே ஒரு relation-ஐ導க்க முடியும்.

Example formula: All A are B மற்றும் All B are C என்றால், All A are C. இந்த rule “Some” மற்றும் “No” போன்ற பிற types-க்கும் பொருந்தும்; ஆனால் direction மற்றும் quantifier type ஒரே மாதிரியாக இருந்தால் மட்டுமே.

Step-by-Step Example

Question

Statements:
1️⃣ எல்லா நாய்களும் விலங்குகள் ஆகும்.
2️⃣ எல்லா விலங்குகளும் உயிருள்ளவை.
3️⃣ எல்லா உயிருள்ளவையும் organisms ஆகும்.

Conclusions:
I. எல்லா நாய்களும் உயிருள்ளவை.
II. எல்லா நாய்களும் organisms ஆகும்.

Options:
A. Conclusion I மட்டும் பின்பற்றுகிறது
B. Conclusion II மட்டும் பின்பற்றுகிறது
C. I மற்றும் II இரண்டும் பின்பற்றுகின்றன
D. I அல்லது II எதுவும் பின்பற்றவில்லை

Solution

  1. Step 1: Statements-ஐ link செய்யுங்கள்

    All dogs ⊂ Animals; All animals ⊂ Living beings; All living beings ⊂ Organisms.

  2. Step 2: Chain relation-ஐ கண்டறியுங்கள்

    Chain-ஐப் பார்த்தால் - Dogs → Animals → Living beings → Organisms, Dogs, Living beings மற்றும் Organisms இரண்டுக்கும் தொடர்ச்சியான “All” relation மூலம் இணைக்கப்படுகின்றன.

  3. Step 3: Conclusions-ஐ மதிப்பீடு செய்யுங்கள்

    (I) “All dogs are living beings” - சரி. ✅ (II) “All dogs are organisms” - extended transitivity மூலம் இதுவும் சரி. ✅

  4. Final Answer:

    I மற்றும் II இரண்டும் பின்பற்றுகின்றன. → Option C

  5. Quick Check:

    All → All → All ⇒ All ✅ (Transitive chain valid)

Quick Variations

1. All + All ⇒ All relation பின்பற்றுகிறது (transitive).

2. All + Some ⇒ “Some” type relation மட்டும் பின்பற்றும்.

3. All + No ⇒ No relation (middle term-ல் contradiction).

4. Some + Some ⇒ definite conclusion இல்லை (possibility மட்டும்).

5. Valid linkage-க்கு middle term ஒன்று predicate ஆகவும் மற்றொன்று subject ஆகவும் ஒருமுறை தோன்ற வேண்டும்.

Trick to Always Use

  • Middle term-ஐ அடையாளம் காணுங்கள் - அதுவே முதல் மற்றும் கடைசி statements-ஐ இணைக்கிறது.
  • இரண்டு statements-மும் ஒரே logical direction-ல் உள்ளதா என்று சரிபார்க்கவும்.
  • Transitivity rules-ஐ பயன்படுத்துங்கள் - All → All = All, All → Some = Some போன்றவை.
  • Direction அல்லது type உடைந்தால், conclusion பின்பற்றாது.

Summary

Summary

  • ஒரு term predicate ஆகவும் மற்றொன்று subject ஆகவும் இணைந்தால் மட்டுமே valid chain உருவாகும்.
  • Transitive “All” statements வலுவான universal conclusions-ஐ தரும்.
  • “Some” அல்லது “No” கலந்தால் chain பலவீனமாகும் அல்லது முற்றிலும் ரத்து ஆகும்.
  • Conclusion எடுக்கும் முன் direction மற்றும் quantity-ஐ எப்போதும் சோதிக்கவும்.

நினைவில் வைத்துக்கொள்ள வேண்டிய உதாரணம்:
All A are B; All B are C ⇒ All A are C ✅

Practice

(1/5)
1. Statements: 1️⃣ All cats are mammals. 2️⃣ All mammals are animals. 3️⃣ Some animals are wild. Conclusions: I. Some cats are wild. II. All cats 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: Link relations

    All Cats ⊂ Mammals ⊂ Animals.

  2. Step 2: Evaluate Conclusion I

    'Some animals are wild' is an existential about Animals; this does not guarantee that the particular animals which are wild include cats. So Conclusion I does not follow. ❌

  3. Step 3: Evaluate Conclusion II

    All Cats ⊂ Mammals and All Mammals ⊂ Animals ⇒ All Cats ⊂ Animals. So Conclusion II follows. ✅

  4. Final Answer:

    Only Conclusion II follows. → Option B

  5. Quick Check:

    All→All yields universal inclusion; an existential about the superset doesn't force overlap with the subset. ✅
Hint: An existential about the superset doesn't imply the subset is part of that existential.
Common Mistakes: Assuming 'Some animals are X' automatically includes every subset of animals.
2. Statements: 1️⃣ Some birds are parrots. 2️⃣ All parrots are talkative. 3️⃣ All talkative beings are noisy. Conclusions: I. Some birds are noisy. II. All noisy beings are parrots.
easy
A. Both I and II follow
B. Only Conclusion I follows
C. Only Conclusion II follows
D. Neither I nor II follows

Solution

  1. Step 1: Form the forward chain

    Some Birds ↔ Parrots; All Parrots ⊂ Talkative; All Talkative ⊂ Noisy.

  2. Step 2: Evaluate Conclusion I

    Some Birds are Parrots → those Parrots are Talkative → therefore those Parrots are Noisy ⇒ Some Birds are Noisy. ✅

  3. Step 3: Evaluate Conclusion II

    'All noisy beings are parrots' is the reverse/universalization of the forward chain and is not supported. ❌

  4. Final Answer:

    Only Conclusion I follows. → Option B

  5. Quick Check:

    Some→All→All gives a forward 'Some'. Reverse universals do not follow. ✅
Hint: Some + All + All → forward Some at extremes.
Common Mistakes: Reversing forward transitive logic into universals.
3. Statements: 1️⃣ All pens are instruments. 2️⃣ Some instruments are musical. 3️⃣ All musical things are enjoyable. Conclusions: I. Some pens are enjoyable. II. Some enjoyable things are instruments.
easy
A. Only Conclusion II follows
B. Both I and II follow
C. Only Conclusion I follows
D. Neither I nor II follows

Solution

  1. Step 1: Map the chain

    All Pens ⊂ Instruments; Some Instruments ↔ Musical; All Musical ⊂ Enjoyable.

  2. Step 2: Evaluate Conclusion I

    Some Instruments are Musical, but those musical instruments may or may not include Pens. So 'Some pens are enjoyable' is not guaranteed. ❌

  3. Step 3: Evaluate Conclusion II

    Some Instruments are Musical and Musical ⊂ Enjoyable ⇒ those Instruments that are Musical are Enjoyable. Thus there exist Enjoyable things that are Instruments ⇒ Some enjoyable things are instruments. ✅

  4. Final Answer:

    Only Conclusion II follows. → Option A

  5. Quick Check:

    All + Some + All gives a guaranteed 'Some' in the middle → Some enjoyable things are instruments. ✅
Hint: Existential in the middle yields 'Some' about the middle and its supersets/subsets only when overlap includes them.
Common Mistakes: Assuming a 'Some' relationship includes all subsets of the superset.
4. Statements: 1️⃣ All books are papers. 2️⃣ All papers are materials. 3️⃣ Some materials are recyclable. Conclusions: I. Some books are recyclable. II. All recyclable things are papers.
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: Form chain

    All Books ⊂ Papers ⊂ Materials.

  2. Step 2: Evaluate Conclusion I

    'Some materials are recyclable' does not guarantee that the recyclable materials include books. The recyclable portion might be disjoint from books, so Some books are recyclable is not certain. ❌

  3. Step 3: Evaluate Conclusion II

    'All recyclable things are papers' is not supported; recyclable things are only a subset of materials and may or may not all be papers. ❌

  4. Final Answer:

    Neither I nor II follows. → Option D

  5. Quick Check:

    Subset chain + existential at superset does not ensure overlap with the subset. ✅
Hint: An existential about the superset can't be assumed to include a particular subset unless stated.
Common Mistakes: Assuming some property of the superset applies to every subset.
5. Statements: 1️⃣ Some engineers are designers. 2️⃣ All designers are creative. 3️⃣ Some creative people are artists. Conclusions: I. Some engineers are artists. II. Some artists are designers.
medium
A. Both I and II follow
B. Neither I nor II follows
C. Only Conclusion I follows
D. Only Conclusion II follows

Solution

  1. Step 1: Understand chain

    Some Engineers ↔ Designers; All Designers ⊂ Creative; Some Creative ↔ Artists.

  2. Step 2: Evaluate Conclusion I

    We have Some Engineers that are Designers and All Designers are Creative; Some Creative are Artists - but there's no guarantee that the particular Creative persons who are Artists overlap with the particular Designers who are Engineers. So 'Some engineers are artists' is not certain. ❌

  3. Step 3: Evaluate Conclusion II

    'Some artists are designers' is also not guaranteed: Some Creative are Artists and All Designers are Creative, but that does not force Designers to overlap the Artists. ❌

  4. Final Answer:

    Neither I nor II follows. → Option B

  5. Quick Check:

    Two separate existential facts about the same middle set do not guarantee overlap between the corresponding particular parts. ✅
Hint: Avoid chaining multiple 'Some' facts expecting guaranteed overlap unless one existential explicitly includes the other.
Common Mistakes: Assuming existence in a superset implies overlap across different existential parts.

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