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Either–Or Type Syllogism

Introduction

Either-Or Type Syllogism என்பது reasoning-இல் மிகவும் logical ஆகவும், கருத்தரீதியாக சற்று tricky ஆகவும் இருக்கும் pattern-களில் ஒன்று. இதில், mutually exclusive but collectively exhaustive conclusions-ஐ நீங்கள் சரியாக அடையாளம் காண்கிறீர்களா என்பதையே சோதிக்கிறது - அதாவது, இரண்டு statements-இல் ஒன்று கண்டிப்பாக true ஆக இருக்க வேண்டும், ஆனால் இரண்டும் ஒரே நேரத்தில் true ஆக இருக்க முடியாது.

இந்த type, banking, SSC, மற்றும் insurance tests போன்ற competitive exams-ல் அடிக்கடி வருகிறது. இதன் logical structure-ஐ தெளிவாக புரிந்துகொண்டால், contradiction மற்றும் complementarity இடையிலான பொதுவான குழப்பங்களை தவிர்க்கலாம்.

Pattern: Either–Or Type Syllogism

Pattern

The key concept: Two conclusions form an “Either-Or” pair only when both are individually false but one of them must be true logically.

Either-Or pair உருவாக வேண்டிய சாதாரண நிபந்தனைகள்:

  • இரண்டுக்கும் same subject and predicate இருக்க வேண்டும்.
  • ஒரு conclusion positive ஆக இருக்க வேண்டும் (e.g., “Some A are B”).
  • மற்றொரு conclusion negative ஆக இருக்க வேண்டும் (e.g., “Some A are not B”).
  • இரண்டும் ஒரே நேரத்தில் true ஆக முடியாது, ஆனால் ஒன்று கண்டிப்பாக true ஆக வேண்டும்.

Step-by-Step Example

Question

Statements:
1️⃣ Some cars are bikes.
2️⃣ No bike is a bus.

Conclusions:
I. Some cars are buses.
II. Some cars are not buses.

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: Interpret given statements

    Some Cars ↔ Bikes; No Bike ↔ Bus ⇒ Cars மற்றும் Buses இடையே indirect relation உள்ளது, ஆனால் தெளிவான relation கிடைக்கவில்லை.

  2. Step 2: Test Conclusion I

    “Some cars are buses” ⇒ Support இல்லை; direct link எதுவும் இல்லை. ❌

  3. Step 3: Test Conclusion II

    “Some cars are not buses” ⇒ இதையும் உறுதிப்படுத்த முடியவில்லை. ❌

  4. Step 4: Apply Either-Or logic

    இரு conclusions-மும் nature-ல் opposite (same subject-predicate, ஒன்று positive, ஒன்று negative). ஆகவே, Either I or II follows. ✅

  5. Final Answer:

    Either I or II follows. → Option C

  6. Quick Check:

    Opposite pair (Some A are B / Some A are not B) → Either-Or ✅

Quick Variations

1. “Some A are B” vs “Some A are not B” - classical Either-Or form.

2. “All A are B” vs “Some A are not B” - இரண்டும் true ஆக முடியாதபோது conditional Either-Or.

3. “No A is B” vs “Some A are B” - direct contradiction மூலம் Either-Or.

4. இரு conclusions-லும் subject மற்றும் predicate ஒரே மாதிரி இருந்தால் மட்டுமே applicable.

Trick to Always Use

  • same subject-predicate pair இருக்கிறதா என்று முதலில் பார்க்கவும்.
  • ஒரு conclusion relation-ஐ accept செய்கிறதா, மற்றொன்று deny செய்கிறதா என்பதை உறுதி செய்யவும்.
  • இரண்டும் ஒரே நேரத்தில் true ஆக முடியாவிட்டால், “Either-Or” possibility-ஐ சோதிக்கவும்.
  • நினைவில் வையுங்கள்: இரண்டும் false ஆக இருப்பது மட்டும் Either-Or-க்கு போதாது - ஒன்று logically possible ஆக இருக்க வேண்டும்.

Summary

Summary

  • Either-Or என்பது, same subject மற்றும் predicate கொண்ட இரண்டு opposite conclusions இருக்கும்போது வரும்.
  • அவை contradictory ஆக இருக்க வேண்டும் (positive vs negative).
  • இரண்டும் ஒரே நேரத்தில் true ஆக முடியாது, ஆனால் ஒன்று கண்டிப்பாக true.
  • Uncertainty உள்ள சூழலில் இரண்டு logical possibilities-ஐ cover செய்ய பயன்படும்.

Example to remember:
Some A are B, Some A are not B ⇒ Either I or II follows ✅

Practice

(1/5)
1. Statements: 1️⃣ Some pens are pencils. 2️⃣ No pencil is eraser. Conclusions: I. Some pens are erasers. II. Some pens are not erasers.
easy
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: Interpret the statements

    Some pens are pencils ⇒ there exists a portion of Pens that is inside Pencils. No pencil is eraser ⇒ Pencils ∩ Erasers = ∅ (pencils are completely outside erasers).

  2. Step 2: Draw the inference

    The pens that lie in the Pencil portion cannot be erasers because Pencils and Erasers are disjoint. Therefore at least some pens are definitely not erasers. ✅

  3. Step 3: Test the other conclusion

    ‘Some pens are erasers’ contradicts the given ‘No pencil is eraser’ for the pens that are pencils, and there is no information about pens outside the pencil portion to support Conclusion I. ❌

  4. Final Answer:

    Only Conclusion II follows. → Option B

  5. Quick Check:

    Some Pens ⊂ Pencils and Pencils ∩ Erasers = ∅ ⇒ those Pens ≠ Erasers → Some pens are not erasers. ✅
Hint: If Some A are B and No B is C ⇒ those Some A are not C.
Common Mistakes: Thinking 'Some' implies membership outside the intersecting subset without checking exclusions.
2. Statements: 1️⃣ All cats are animals. 2️⃣ Some animals are not dogs. Conclusions: I. Some cats are dogs. II. Some cats are not dogs.
easy
A. Either I or II follows
B. Only Conclusion II follows
C. Both I and II follow
D. Neither I nor II follows

Solution

  1. Step 1: Identify the relation

    All Cats ⊂ Animals; Some Animals are not Dogs ⇒ uncertain relation between Cats and Dogs.

  2. Step 2: Test conclusions

    ‘Some cats are dogs’ ❌ not supported, ‘Some cats are not dogs’ ❌ also not confirmed.

  3. Step 3: Apply Either-Or logic

    Same subject-predicate (Cats-Dogs) with one positive and one negative ⇒ Either-Or condition satisfied. ✅

  4. Final Answer:

    Either I or II follows. → Option A

  5. Quick Check:

    Uncertain relation + opposite conclusions = Either-Or. ✅
Hint: Uncertain relation + contradictory conclusions → Either-Or.
Common Mistakes: Assuming one definite truth.
3. Statements: 1️⃣ Some books are pages. 2️⃣ All pages are papers. Conclusions: I. Some books are papers. II. Some books are not papers.
easy
A. Neither I nor II follows
B. Only Conclusion I follows
C. Only Conclusion II follows
D. Either I or II follows

Solution

  1. Step 1: Combine statements

    Some Books ↔ Pages; All Pages ⊂ Papers ⇒ therefore, Some Books ⊂ Papers. ✅

  2. Step 2: Evaluate conclusions

    Conclusion I (‘Some books are papers’) follows logically. ✅ Conclusion II (‘Some books are not papers’) contradicts the result. ❌

  3. Final Answer:

    Only Conclusion I follows. → Option B

  4. Quick Check:

    Some + All ⇒ Some → valid conclusion. ✅
Hint: Some + All ⇒ Some.
Common Mistakes: Marking Either-Or when one conclusion is valid.
4. Statements: 1️⃣ Some fruits are mangoes. 2️⃣ All mangoes are sweet. Conclusions: I. Some fruits are not sweet. II. All sweet things are fruits.
medium
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: Analyze premises

    Some Fruits ⊂ Mangoes; All Mangoes ⊂ Sweet ⇒ Fruits ⊂ Sweet partially, but no universal link established.

  2. Step 2: Test conclusions

    ‘Some fruits are not sweet’ ❌ contradicts given; ‘All sweet things are fruits’ ❌ goes beyond data. Neither conclusion is valid.

  3. Final Answer:

    Neither I nor II follows. → Option D

  4. Quick Check:

    If data doesn’t cover totality, avoid universal conclusions. ✅
Hint: If statements are unrelated or lack overlap, neither conclusion follows.
Common Mistakes: Applying Either-Or without opposite relation.
5. Statements: 1️⃣ Some laptops are mobiles. 2️⃣ Some mobiles are not gadgets. Conclusions: I. Some laptops are gadgets. II. Some laptops are not gadgets.
medium
A. Only Conclusion I follows
B. Either I or II follows
C. Only Conclusion II follows
D. Neither I nor II follows

Solution

  1. Step 1: Understand statements

    Some Laptops ↔ Mobiles; Some Mobiles are not Gadgets ⇒ Uncertain link between Laptops and Gadgets.

  2. Step 2: Check conclusions

    ‘Some laptops are gadgets’ ❌ not proven; ‘Some laptops are not gadgets’ ❌ also unproven individually.

  3. Step 3: Apply Either-Or condition

    Both share same subject-predicate (Laptops-Gadgets) but are opposites. Both cannot be true, one must be true. ✅

  4. Final Answer:

    Either I or II follows. → Option B

  5. Quick Check:

    ‘Some A are B’ vs ‘Some A are not B’ with uncertain relation ⇒ Either-Or applies. ✅
Hint: When two opposite conclusions (positive & negative) share same terms and data doesn’t confirm either - choose Either-Or.
Common Mistakes: Marking one conclusion as true without checking the uncertainty condition.

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