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Basic Two-Statement Syllogism

Introduction

Basic Two-Statement Syllogism logical reasoning का सबसे मूलभूत पैटर्न है, जो लगभग हर aptitude exam में पूछा जाता है। इसमें दो factual statements दिए जाते हैं और यह जाँचना होता है कि कौन-से conclusion(s) उनसे logically follow करते हैं।

इस पैटर्न को समझने से आप direct logical relations को Venn diagrams या conceptual reasoning की मदद से evaluate करना सीखते हैं।

Pattern: Basic Two-Statement Syllogism

Pattern

मुख्य अवधारणा: दो categories के बीच “All”, “Some”, और “No” वाले direct या transitive संबंधों को test करना।

आमतौर पर दो statements और कई conclusions दिए जाते हैं, और आपको तय करना होता है कि कौन-से conclusions निश्चित रूप से follow करते हैं।

Step-by-Step Example

Question

Statements:
1️⃣ All cats are animals.
2️⃣ Some animals are dogs.

Conclusions:
I. Some cats are dogs.
II. All dogs are animals.

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: संबंध को visualize करें

    “All cats are animals” → Cats का circle Animals के अंदर पूरी तरह आता है।
    “Some animals are dogs” → Dogs का circle Animals से आंशिक रूप से overlap करता है, पर Cats से जरूरी नहीं कि overlap करे।

  2. Step 2: Conclusion I जाँचें

    “Some cats are dogs” → यह जरूरी नहीं है, क्योंकि Cats और Dogs के बीच direct overlap दिखाया नहीं गया है। ❌

  3. Step 3: Conclusion II जाँचें

    “All dogs are animals” → “Some animals are dogs” यह नहीं कहता कि Dogs पूरी तरह Animals में आते हैं - केवल partial overlap बताया गया है। इसलिए यह भी निश्चित नहीं है। ❌

  4. Final Answer:

    Neither I nor II follows. → Option D

  5. Quick Check:

    “Some animals are dogs” ≠ “All dogs are animals.”
    Cats और Dogs के बीच कोई definite संबंध नहीं दिया गया। इसलिए दोनों conclusions invalid हैं। ✅

Quick Variations

1. दोनों statements “All” से शुरू हों (transitive logic)।

2. किसी एक statement में “Some” हो तो partial overlap बनता है।

3. “All-Some” या “Some-All” combinations conclusions को सीमित करते हैं।

4. Positive-Negative conclusions हों तो “Either-Or” टेस्ट किया जाता है।

Trick to Always Use

  • तीन circles (A, B, C) का simple Venn diagram बनाकर relation जल्दी समझें।
  • “All + All” में transitive rule लागू करें (All A are C)।
  • “All + Some” में कोई universal (“All”) conclusion follow नहीं करता।
  • General knowledge कभी न उपयोग करें - केवल statements के logic पर निर्भर रहें।

Summary

Summary

  • Statements के type - “All”, “Some”, “No” - को ध्यान से पढ़ें।
  • Decision लेने से पहले Venn diagram का सहारा लें।
  • “All + All” में transitive logic चलता है, जबकि “All + Some” conclusions को सीमित करता है।
  • सिर्फ दिए गए statements के आधार पर ही valid follow-through तय करें।

याद रखने के लिए उदाहरण:
All A are B; All B are C ⇒ All A are C ✅

Practice

(1/5)
1. Statements: 1️⃣ All birds are animals. 2️⃣ Some animals are reptiles. Conclusions: I. Some birds are reptiles. II. All reptiles 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: Visualize sets

    ‘All birds are animals’ ⇒ Birds fully inside Animals. ‘Some animals are reptiles’ ⇒ Reptiles partly overlap with Animals, but their exact position relative to Birds is unknown.

  2. Step 2: Test Conclusion I

    ‘Some birds are reptiles’ ⇒ Not necessarily true, as no direct overlap between Birds and Reptiles is established. ❌

  3. Step 3: Test Conclusion II

    ‘All reptiles are animals’ ⇒ Not proven, since ‘Some animals are reptiles’ only shows partial overlap, not total inclusion. ❌

  4. Final Answer:

    Neither Conclusion I nor II follows. → Option D

  5. Quick Check:

    Both statements show only partial and one-directional information; no definitive overlap or full inclusion between Birds and Reptiles. Hence, neither conclusion follows. ✅
Hint: ‘All + Some’ → Never assume total inclusion or guaranteed overlap.
Common Mistakes: Treating 'Some animals are reptiles' as 'All reptiles are animals'.
2. Statements: 1️⃣ All apples are fruits. 2️⃣ All fruits are sweet. Conclusions: I. All apples are sweet. II. Some sweet things are fruits.
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: Establish relations

    ‘All apples are fruits’; ‘All fruits are sweet.’

  2. Step 2: Transitive logic

    If all apples are fruits and all fruits are sweet ⇒ All apples are sweet. ✅

  3. Step 3: Partial inclusion

    ‘All fruits are sweet’ implies ‘Some sweet things are fruits.’ ✅

  4. Final Answer:

    Both I and II follow. → Option C

  5. Quick Check:

    Apples ⊂ Fruits ⊂ Sweet ⇒ both conclusions logically hold. ✅
Hint: ‘All + All’ ⇒ Both direct and partial conclusions are valid.
Common Mistakes: Missing that ‘All’ implies ‘Some’.
3. Statements: 1️⃣ Some pens are pencils. 2️⃣ All pencils are stationery. Conclusions: I. Some stationery are pens. II. All pens are stationery.
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

    ‘Some pens are pencils’; ‘All pencils are stationery.’

  2. Step 2: Link the chain

    Those pens which are pencils are definitely stationery ⇒ Some stationery are pens. ✅

  3. Step 3: Test universal relation

    ‘All pens are stationery’ is not given, so cannot conclude. ❌

  4. Final Answer:

    Only Conclusion I follows. → Option A

  5. Quick Check:

    Partial overlap confirmed between pens and stationery. ✅
Hint: If ‘Some A are B’ and ‘All B are C’ ⇒ ‘Some C are A’.
Common Mistakes: Assuming all A are C from partial premise.
4. Statements: 1️⃣ All doctors are professionals. 2️⃣ Some professionals are teachers. Conclusions: I. Some teachers are doctors. II. Some professionals are 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: Visualize relationship

    Doctors ⊂ Professionals; Some Professionals ↔ Teachers.

  2. Step 2: Check Conclusion I

    ‘Some teachers are doctors’ → No direct link, not valid. ❌

  3. Step 3: Check Conclusion II

    ‘Some professionals are doctors’ → True because all doctors are professionals, so at least some professionals are doctors. ✅

  4. Final Answer:

    Only Conclusion II follows. → Option B

  5. Quick Check:

    Doctors inside professionals; hence some professionals are definitely doctors. ✅
Hint: ‘All A are B’ ensures ‘Some B are A’.
Common Mistakes: Linking Teachers and Doctors without direct relation.
5. Statements: 1️⃣ All engineers are graduates. 2️⃣ Some graduates are artists. Conclusions: I. Some engineers are artists. II. Some artists are graduates.
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: Identify relations

    ‘All engineers are graduates’; ‘Some graduates are artists.’

  2. Step 2: Test Conclusion I

    ‘Some engineers are artists’ → No link between engineers and artists. ❌

  3. Step 3: Test Conclusion II

    ‘Some artists are graduates’ → True by reversing the second statement. ✅

  4. Final Answer:

    Only Conclusion II follows. → Option B

  5. Quick Check:

    Artists ↔ Graduates confirmed; Engineers separate from artists. ✅
Hint: ‘Some A are B’ ⇒ ‘Some B are A’ is always true.
Common Mistakes: Assuming Engineers connect to Artists through Graduates.

Mock Test

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