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Only / Only Few Type Syllogism

Introduction

Only / Only Few Type Syllogism ऐसे statements पर आधारित होता है जिन्हें logically दोबारा interpret करना पड़ता है। “Only” और “Only a few” जैसे शब्द statements की दिशा बदल देते हैं, जिससे learners अक्सर भ्रमित हो जाते हैं।

इन conversions को समझना ज़रूरी है क्योंकि यह standard syllogism forms (“All”, “Some”, “No”) की सामान्य structure को उलट देता है। सही conversion सीखने के बाद conclusions को test करना आसान हो जाता है।

Pattern: Only / Only Few Type Syllogism

Pattern

मुख्य अवधारणा: “Only A are B” का वास्तविक अर्थ है “All B are A”. यानी term order उलट जाता है।

इसी तरह, “Only a few A are B” का मतलब है कुछ A, B हैं लेकिन सभी A, B नहीं हैं - यह quantity को restrict करता है, जिसमें partial inclusion का संबंध बनता है।

Step-by-Step Example

Question

Statement: Only cats are pets.

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

Options:
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: Statement को सही ढंग से interpret करें

    “Only cats are pets” ⇒ Logical conversion ⇒ “All pets are cats.” इसका यह अर्थ नहीं है कि “All cats are pets.”

  2. Step 2: Conclusion I test करें

    “All pets are cats” ⇒ Converted meaning से पूरी तरह match करता है। ✅

  3. Step 3: Conclusion II test करें

    “Some cats are pets” ⇒ अगर सभी pets cats हैं, तो निश्चित ही कुछ cats pets होंगी। यह भी सही है। ✅

  4. Final Answer:

    Both I and II follow. → Option C

  5. Quick Check:

    “Only cats are pets” ≡ “All pets are cats” ⇒ इससे “Some cats are pets” स्वतः true हो जाता है। ✅

Quick Variations

1. “Only A are B” → convert to “All B are A”.

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

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

4. ऐसे questions में positive और negative logic दोनों होते हैं - दोनों direction ध्यान से test करें।

Trick to Always Use

  • “Only” से शुरू होने वाले statements को हमेशा reverse कर दें। उदाहरण: “Only A are B” → “All B are A”.
  • “Only a few A are B” के लिए दो हिस्से लिखें: “Some A are B” + “Some A are not B.”
  • कभी भी “Only A are B” को “All A are B” मत समझें - यह common mistake है।
  • Visualization: “Only A are B” का मतलब B-circle, A-circle के अंदर आता है।

Summary

Summary

  • “Only A are B” ⇒ “All B are A” (reversed structure).
  • “Only a few A are B” ⇒ partial overlap + partial exclusion।
  • “Only” statements को convert किए बिना conclusions test न करें।
  • Negative part (“Not all”) secondary conclusions को decide करने में मदद करता है।

याद रखने के लिए उदाहरण:
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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