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Few / Most Quantifier Type

Introduction

Few / Most Quantifier Type Syllogisms இல், பாரம்பரியமான “All,” “Some,” அல்லது “No” என்பவற்றுக்கு பதிலாக “Few,” “Most,” “Majority,” “Almost all,” போன்ற non-standard quantifiers பயன்படுத்தப்படுகின்றன. இவை பகுதி சேர்க்கை அல்லது பெரும்பான்மை / சிறுபான்மை தொடர்புகளை சுட்டிக்காட்டுகின்றன.

இத்தகைய statements advanced reasoning tests-ல் அடிக்கடி காணப்படுகின்றன; அதனால் கவனமான விளக்கம் அவசியம். இந்த quantifiers-ன் சுமார் பொருளை புரிந்துகொள்வதே conclusions definite ஆவையா அல்லது possible ஆவையா என்பதை தீர்மானிக்க முக்கியமானது.

Pattern: Few / Most Quantifier Type

Pattern

முக்கிய சவால் என்பது “Few” மற்றும் “Most” என்பவை “Some,” “All,” மற்றும் “No” உடன் எவ்வாறு logic-ஆக தொடர்பு கொண்டுள்ளன என்பதை புரிந்துகொள்வதே.

  • Few → “Some, but less than half” எனப் பொருள். அதனால் இது எப்போதும் “Some” என்பதை குறிக்கும்.
  • Most → “More than half” எனப் பொருள். இதுவும் “Some” என்பதை குறிக்கிறது.
  • Few not → ஒரு சிறிய பகுதி மற்ற set-க்கு சேர்ந்ததல்ல என்பதை குறிக்கிறது.
  • Most not → பெரும்பான்மை பகுதி சேர்ந்ததல்ல; ஆனால் எல்லாம் அல்ல.

ஆகவே, “Few” மற்றும் “Most” statements இரண்டும் existence (Some)-ஐ உறுதி செய்கின்றன; ஆனால் universality (All)-ஐ நிரூபிக்காது.

Step-by-Step Example

Question

Statements:
1️⃣ Most students are hardworking.
2️⃣ Some hardworking people are successful.

Conclusions:
I. Some students are successful.
II. All students are successful.

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 statements

    “Most students are hardworking” என்பதன் பொருள் Students-ன் பெரும்பகுதி ⊂ Hardworking.
    “Some hardworking are successful” என்பதன் பொருள் Hardworking மற்றும் Successful இடையில் பகுதி overlap உள்ளது.

  2. Step 2: Derive indirect link

    Students பெரும்பகுதி Hardworking உடன் தொடர்பில் இருப்பதால், மேலும் சில Hardworking Successful ஆக இருப்பதால், சில Students Successful ஆக இருப்பது possible.

  3. Step 3: Check conclusions

    Conclusion I (“Some students are successful”) possible மற்றும் consistent ஆகும்.
    Conclusion II (“All students are successful”) ஆதரிக்கப்படவில்லை.

  4. Final Answer:

    Only Conclusion I follows. → Option A

  5. Quick Check:

    “Most” எப்போதும் existence-ஐ உறுதி செய்கிறது → Some valid overlap. ✅

Quick Variations

  • 1. Few-Few Chain: “Few A are B” + “Few B are C” → A மற்றும் C இடையிலான தொடர்பு uncertain.
  • 2. Most-Some Chain: “Most A are B” + “Some B are C” → “Some A are C” possible; definite அல்ல.
  • 3. Few-Not Relation: “Few A are not B” → சில A-கள் B; சில இல்லை (dual condition).
  • 4. Most-Not Relation: “Most A are not B” → பெரும்பான்மை விலக்கம்; universal negative-க்கு எதிரானது.

Trick to Always Use

  • “Few” மற்றும் “Most” எப்போதும் “Some” என்பதைக் குறிக்கும்.
  • “Few” என்பது ஒருபோதும் “None” அல்ல.
  • “Most” என்பது ஒருபோதும் “All” என்பதை உறுதி செய்யாது.
  • Possibility-ஐ சோதிக்க extreme positions assume செய்து contradiction வருகிறதா என்று பாருங்கள்.
  • இரண்டு statements-ம் partial ஆக இருந்தால், definite conclusion இல்லை - possibility-based conclusions மட்டுமே.

Summary

Summary

  • “Few” → Some, ஆனால் All அல்ல.
  • “Most” → More than half, ஆனால் All அல்ல.
  • இரண்டும் existence (Some)-ஐ குறிக்கும்.
  • Definite conclusions அரிது; logic possibility-யை சோதிக்க வேண்டும்.

நினைவில் வைக்க வேண்டிய உதாரணம்:
Most A are B; Some B are C ⇒ Some A are possibly C. ✅

Practice

(1/5)
1. Statements: 1️⃣ Most teachers are readers. 2️⃣ Some readers are writers. Conclusions: I. Some teachers are writers. II. All readers are teachers.
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 statements

    Most Teachers ⊂ Readers (large overlap); Some Readers ↔ Writers (partial overlap).

  2. Step 2: Link logically

    Teachers → Readers → Writers ⇒ overlap possible ⇒ Some Teachers may be Writers.

  3. Step 3: Validate conclusions

    Conclusion I (‘Some teachers are writers’) is possible and consistent. ✅
    Conclusion II (‘All readers are teachers’) reverses direction - invalid. ❌

  4. Final Answer:

    Only Conclusion I follows. → Option A

  5. Quick Check:

    Most + Some ⇒ Some (Possible). ✅
Hint: Most + Some ⇒ Possibility of Some overlap.
Common Mistakes: Assuming ‘Most’ implies ‘All’.
2. Statements: 1️⃣ Few students are artists. 2️⃣ All artists are creative. Conclusions: I. Few students are creative. II. Some students are creative.
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

    Few Students ⊂ Artists ⇒ Some Students are Artists (but less than half). All Artists ⊂ Creative ⇒ All Artists are within Creative.

  2. Step 2: Derive inference

    Some (few) Students are Artists → All Artists are Creative ⇒ Those few Students are also Creative.

  3. Step 3: Verify conclusions

    Conclusion I (‘Few students are creative’) is valid, as few implies small subset. ✅
    Conclusion II (‘Some students are creative’) is also valid, because ‘Few’ implies ‘Some’. ✅

  4. Final Answer:

    Both I and II follow. → Option C

  5. Quick Check:

    Few always includes Some. ✅
Hint: Few ⇒ Some (always true).
Common Mistakes: Treating ‘Few’ as uncertain existence.
3. Statements: 1️⃣ Most engineers are logical. 2️⃣ Few logical people are artists. Conclusions: I. Some engineers are artists. II. Some engineers are not artists.
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: Understand statements

    Most Engineers ⊂ Logical; Few Logical ↔ Artists ⇒ small overlap between Logical and Artists.

  2. Step 2: Derive relation

    Since Logical partly overlaps Artists, some Engineers may not be Artists (because only few Logical people are). So 'Some Engineers are not Artists' is possible.

  3. Final Answer:

    Only Conclusion II follows. → Option B

  4. Quick Check:

    ‘Few’ restricts overlap ⇒ Some not relation valid. ✅
Hint: When ‘Few’ reduces overlap, ‘Some not’ conclusions often hold.
Common Mistakes: Assuming large overlap from ‘Most’.
4. Statements: 1️⃣ Few managers are leaders. 2️⃣ Most leaders are confident. Conclusions: I. Some managers are confident. II. No manager is confident.
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: Interpret

    Few Managers ⊂ Leaders (some Managers are Leaders). Most Leaders ⊂ Confident (large part of Leaders are Confident).

  2. Step 2: Link

    The Managers who are Leaders may also be part of the Confident group.

  3. Step 3: Conclusion

    Some Managers are Confident → follows logically. 'No manager is confident' contradicts it. ❌

  4. Final Answer:

    Only Conclusion I follows. → Option A

  5. Quick Check:

    Few + Most ⇒ Some. ✅
Hint: Few + Most ⇒ Some (positive possibility).
Common Mistakes: Assuming few = negligible ⇒ no overlap.
5. Statements: 1️⃣ Most politicians are orators. 2️⃣ Few orators are honest. Conclusions: I. Some politicians are honest. II. Some politicians are not honest.
medium
A. Only Conclusion I follows
B. Only Conclusion II follows
C. Either I or II follows
D. Both I and II follow

Solution

  1. Step 1: Decode statements

    Most Politicians ⊂ Orators; Few Orators ⊂ Honest ⇒ small overlap between Orators and Honest.

  2. Step 2: Derive link

    Politicians majorly fall in Orators, but only a few Orators are Honest ⇒ some Politicians may not be Honest.

  3. Step 3: Verify

    ‘Some politicians are honest’ is possible but not guaranteed. ‘Some politicians are not honest’ logically follows.

  4. Final Answer:

    Only Conclusion II follows. → Option B

  5. Quick Check:

    Most + Few ⇒ Some not valid. ✅
Hint: Few ⇒ limited overlap ⇒ Some not likely follows.
Common Mistakes: Assuming honesty extends to all Orators.

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