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Only / Only Few Type Syllogism

Introduction

Only / Only Few Type Syllogism pattern-ல் உள்ள statements, மதிப்பீடு செய்யும் முன் logical-ஆக மீண்டும் விளக்கப்பட வேண்டியவை ஆகும். “Only” மற்றும் “Only a few” போன்ற சொற்கள், statement-ன் logical direction-ஐ மாற்றுவதால், மாணவர்களுக்கு குழப்பம் ஏற்படுகிறது.

இந்த conversions-ஐ சரியாக புரிந்துகொள்வது மிகவும் முக்கியம்; ஏனெனில் இது வழக்கமான syllogism forms (“All”, “Some”, “No”) ஆகியவற்றின் சாதாரண அமைப்பை மாற்றி விடுகிறது. சரியான conversion தெரிந்தவுடன், conclusions-ஐ சோதிப்பது எளிதாகிவிடும்.

Pattern: Only / Only Few Type Syllogism

Pattern

The key concept: “Only A are B” என்பது logical-ஆக “All B are A” என்பதைக் குறிக்கும். இதில் terms-ன் வரிசை மாற்றப்படுகிறது.

அதேபோல், “Only a few A are B” என்றால் சில A-கள் B ஆகும் ஆனால் எல்லா A-களும் B ஆகாது என்பதாகும். இந்த statement quantity-ஐ கட்டுப்படுத்தி, ஒரு partial inclusion relation-ஐ உருவாக்குகிறது.

Step-by-Step Example

Question

Statement: Only cats are pets.

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

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: Statement-ஐ சரியாக விளக்குங்கள்

    “Only cats are pets” ⇒ logical-ஆக reverse செய்தால் ⇒ “All pets are cats.” இதன் அர்த்தம் “All cats are pets” அல்ல.

  2. Step 2: Conclusion I-ஐ சோதிக்கவும்

    “All pets are cats” ⇒ இது converted meaning-ஐப் பொருந்துகிறது. ✅

  3. Step 3: Conclusion II-ஐ சோதிக்கவும்

    “Some cats are pets” ⇒ சரி; ஏனெனில் எல்லா pets-உம் cats என்றால், கண்டிப்பாக சில cats pets ஆக இருக்கும். ✅

  4. Final Answer:

    I மற்றும் II இரண்டும் பின்பற்றுகின்றன. → Option C

  5. Quick Check:

    “Only cats are pets” ≡ “All pets are cats” ⇒ தானாகவே “Some cats are pets” என்பதைக் குறிக்கும். ✅

Quick Variations

1. “Only A are B” → “All B are A” என்பதாகும்.

2. “Only some A are B” → “Some A are B” ஆனால் “Not all A are B.”

3. “Only a few A are B” → “Some A are B” மற்றும் “Some A are not B.”

4. இந்த questions-ல் positive மற்றும் negative logic கலந்து வரும் - இரு திசைகளையும் கவனமாகச் சரிபார்க்கவும்.

Trick to Always Use

  • “Only” என்று தொடங்கும் sentence-ஐ எப்போதும் reverse செய்யுங்கள். Example: “Only A are B” → “All B are A.”
  • “Only a few A are B” என்றால் இரண்டு பகுதிகளாக எழுதுங்கள்: “Some A are B” + “Some A are not B.”
  • “Only A are B” என்பதைக் “All A are B” என்று ஒருபோதும் பொருள் கொள்ள வேண்டாம் - இது பொதுவான தவறு.
  • Sets-ஐ visualize செய்யுங்கள்: “Only A are B” என்றால் B-circle, A-circle-ன் உள்ளே இருக்கும்.

Summary

Summary

  • “Only A are B” ⇒ “All B are A” (reverse structure).
  • “Only a few A are B” ⇒ partial overlap மற்றும் partial exclusion.
  • Conclusions-ஐ சோதிக்கும் முன் “Only” statements-ஐ எப்போதும் convert செய்யுங்கள்.
  • Negative பகுதி (“not all”) secondary valid conclusions-ஐ கண்டறிய உதவும்.

நினைவில் வைத்துக்கொள்ள வேண்டிய உதாரணம்:
Only dogs are pets ⇒ All pets are dogs ✅

Practice

(1/5)
1. Statement: Only teachers are readers. Conclusions: I. All readers are teachers. II. Some teachers are readers.
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 the statement

    “Only teachers are readers” means “All readers are teachers.” It does not mean “All teachers are readers.”

  2. Step 2: Test Conclusion I

    ‘All readers are teachers’ is exactly the logical conversion of the statement. ✅

  3. Step 3: Test Conclusion II

    ‘Some teachers are readers’ is automatically true, because if all readers are teachers, then there exists overlap (some teachers are readers). ✅

  4. Final Answer:

    Both I and II follow. → Option C

  5. Quick Check:

    Readers ⊂ Teachers ⇒ both ‘All readers are teachers’ and ‘Some teachers are readers’ hold. ✅
Hint: ‘Only A are B’ ⇒ All B are A; Some A are B (automatic).
Common Mistakes: Misreading as ‘All teachers are readers.’
2. Statement: Only engineers are scientists. Conclusions: I. All scientists are engineers. II. Some engineers are scientists.
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: Convert correctly

    ‘Only engineers are scientists’ ⇒ ‘All scientists are engineers.’

  2. Step 2: Test Conclusion I

    ‘All scientists are engineers’ is directly valid. ✅

  3. Step 3: Test Conclusion II

    ‘Some engineers are scientists’ is also valid because at least those who are scientists belong to engineers. ✅

  4. Final Answer:

    Both I and II follow. → Option C

  5. Quick Check:

    Scientists ⊂ Engineers ⇒ overlap guaranteed. ✅
Hint: ‘Only A are B’ → ‘All B are A’ + ‘Some A are B’.
Common Mistakes: Forgetting partial overlap derived from conversion.
3. Statement: Only a few fruits are sweet. Conclusions: I. Some fruits are sweet. II. Some fruits are not sweet.
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

    ‘Only a few fruits are sweet’ means ‘Some fruits are sweet’ and ‘Some fruits are not sweet.’

  2. Step 2: Test Conclusion I

    ‘Some fruits are sweet’ ⇒ directly part of statement. ✅

  3. Step 3: Test Conclusion II

    ‘Some fruits are not sweet’ ⇒ also implied by ‘only a few’. ✅

  4. Final Answer:

    Both I and II follow. → Option C

  5. Quick Check:

    Partial inclusion + partial exclusion both true. ✅
Hint: ‘Only a few A are B’ ⇒ Some A are B + Some A are not B.
Common Mistakes: Treating ‘Only a few’ as ‘All’.
4. Statement: Only doctors are specialists. Conclusions: I. All specialists are doctors. II. Some specialists are not 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: Convert the statement

    ‘Only doctors are specialists’ ⇒ ‘All specialists are doctors.’

  2. Step 2: Test Conclusion I

    Matches exactly ⇒ valid. ✅

  3. Step 3: Test Conclusion II

    Contradicts the meaning; all specialists are inside doctors, so none are outside. ❌

  4. Final Answer:

    Only Conclusion I follows. → Option A

  5. Quick Check:

    Specialists ⊂ Doctors ⇒ no contradiction possible. ✅
Hint: Reverse ‘Only A are B’ to ‘All B are A’.
Common Mistakes: Assuming ‘Only’ applies to both sides equally.
5. Statement: Only a few students are intelligent. Conclusions: I. Some students are intelligent. II. Some students are not intelligent.
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: Break the phrase

    ‘Only a few students are intelligent’ implies two parts: ‘Some students are intelligent’ + ‘Some students are not intelligent.’

  2. Step 2: Evaluate Conclusion I

    ‘Some students are intelligent’ ⇒ valid. ✅

  3. Step 3: Evaluate Conclusion II

    ‘Some students are not intelligent’ ⇒ valid. ✅

  4. Final Answer:

    Both I and II follow. → Option C

  5. Quick Check:

    ‘Only a few’ means partial inclusion + partial exclusion ⇒ both valid. ✅
Hint: Always split ‘Only a few’ into two complementary conclusions.
Common Mistakes: Forgetting to include the negative component.

Mock Test

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