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Premise–Conclusion Single Chain

Introduction

कई logical reasoning questions linked premises पर आधारित होते हैं - जहाँ एक statement दूसरे से logically जुड़कर एक chain बनाता है। Skill यह है कि इस chain को सही तरह से trace करके वह conclusion पहचानें जो naturally निकलता है।

यह pattern महत्वपूर्ण है क्योंकि यह syllogistic reasoning की नींव है, जिसमें हम transitive logic का उपयोग करके indirect relations निकालते हैं (A → B → C ⇒ A → C)।

Pattern: Premise–Conclusion Single Chain

Pattern

जब दो statements में कोई common term होता है, इन्हें logically combine करके सीधा conclusion निकाला जाता है।

Typical structure:
If “All A are B” और “All B are C”, then All A are C। इसे transitive deduction rule कहा जाता है।

Step-by-Step Example

Question

Statements:
1️⃣ All dogs are mammals.
2️⃣ All mammals are animals.

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

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: Premises समझें

    Premise 1: All dogs ⊂ mammals.
    Premise 2: All mammals ⊂ animals.

  2. Step 2: Common term पहचानें

    Common (middle) term है - “mammals”。 Chain: dogs → mammals → animals ⇒ dogs → animals

  3. Step 3: Conclusions test करें

    I. All dogs are animals → ✅ logically follow करता है।
    II. All animals are dogs → ❌ logic reverse कर देता है; valid नहीं है।

  4. Final Answer:

    Only Conclusion I follows → Option A

  5. Quick Check:

    Visual chain: Dogs → Mammals → Animals ⇒ Dogs → Animals ✅

Quick Variations

1. “Some” या “No” वाले statements के साथ chain formation थोड़ी अलग होती है।

2. Reverse-chain traps - हमेशा direction check करें।

3. लंबी chains भी बन सकती हैं: A → B → C → D → …

4. “No A is B” जैसी negatives में transitivity की जगह elimination logic चलता है।

Trick to Always Use

  • Step 1: Middle term पहचानें जो दोनों premises को जोड़ता है।
  • Step 2: First और last terms को logically connect करें - middle term drop कर दें।
  • Step 3: Direction कभी reverse न करें - “All A are B” का मतलब “All B are A” नहीं होता।

Summary

Summary

  • Premise-Conclusion chains में transitive logic चलता है: A → B और B → C ⇒ A → C।
  • Middle term logical linking में मदद करता है।
  • Direction का हमेशा ध्यान रखें - reversal गलत conclusion देता है।
  • Conclusion वही valid है जो chain की direction और scope को preserve करता है।

Example याद रखें:
Statements: All cars are vehicles. All vehicles are machines.
Conclusion: All cars are machines → Option A ✅

Practice

(1/5)
1. Statements: All parrots are birds. All birds are animals. Conclusions: I. All parrots are animals. II. All animals are parrots. Which of the following options is correct?
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: Understand premises

    All parrots ⊂ Birds, and All Birds ⊂ Animals.

  2. Step 2: Apply transitive rule

    Parrots → Birds → Animals ⇒ Parrots → Animals.

  3. Step 3: Evaluate conclusions

    I. All parrots are animals → ✅ Correct.
    II. All animals are parrots → ❌ Reverse; invalid.

  4. Final Answer:

    Only Conclusion I follows → Option A

  5. Quick Check:

    Link chain is one-directional - Parrots ⊂ Animals ✅
Hint: Link the ends and keep direction same - never reverse the logic.
Common Mistakes: Reversing conclusion and assuming ‘All animals are parrots’.
2. Statements: All cars are vehicles. All vehicles are machines. Conclusions: I. All machines are cars. II. All cars are machines. Which of the following options is correct?
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: Identify premises

    Cars ⊂ Vehicles; Vehicles ⊂ Machines.

  2. Step 2: Apply transitivity

    Cars → Vehicles → Machines ⇒ Cars → Machines.

  3. Step 3: Check conclusions

    I. All machines are cars → ❌ Reverse; invalid.
    II. All cars are machines → ✅ True.

  4. Final Answer:

    Only Conclusion II follows → Option B

  5. Quick Check:

    Direction Cars → Machines holds true ✅
Hint: If A ⊂ B and B ⊂ C ⇒ A ⊂ C. Reverse not valid.
Common Mistakes: Confusing direction of inclusion (‘All’ reversed).
3. Statements: All pens are tools. All tools are useful. Conclusions: I. All pens are useful. II. All useful things are tools. Which of the following options is correct?
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: Decode statements

    Pens ⊂ Tools, Tools ⊂ Useful.

  2. Step 2: Apply transitive deduction

    Pens → Tools → Useful ⇒ Pens → Useful.

  3. Step 3: Test conclusions

    I. All pens are useful → ✅ True.
    II. All useful things are tools → ❌ Reverse; not supported.

  4. Final Answer:

    Only Conclusion I follows → Option A

  5. Quick Check:

    Pens → Useful confirmed; reverse logic invalid ✅
Hint: Link start to end; ignore the middle term once combined.
Common Mistakes: Assuming converse ‘All useful are tools’.
4. Statements: All rivers are water bodies. All water bodies are natural resources. Conclusions: I. All rivers are natural resources. II. Some natural resources are rivers. Which of the following options is correct?
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: Understand link

    Rivers ⊂ Water bodies; Water bodies ⊂ Natural resources.

  2. Step 2: Combine logically

    Rivers → Natural resources (transitive).

  3. Step 3: Check conclusions

    I. All rivers are natural resources → ✅ True.
    II. Some natural resources are rivers → ✅ Also true (part of first statement).

  4. Final Answer:

    Both I and II follow → Option C

  5. Quick Check:

    ‘All’ implies ‘some’ also true ✅
Hint: ‘All’ automatically includes ‘Some’.
Common Mistakes: Forgetting that ‘All A are B’ also means ‘Some B are A’.
5. Statements: All laptops are computers. All computers are electronic devices. Conclusions: I. All laptops are electronic devices. II. All electronic devices are computers. Which of the following options is correct?
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 hierarchy

    Laptops ⊂ Computers; Computers ⊂ Electronic devices.

  2. Step 2: Apply transitive rule

    Laptops → Computers → Electronic devices ⇒ Laptops → Electronic devices.

  3. Step 3: Verify conclusions

    I. All laptops are electronic devices → ✅ Correct.
    II. All electronic devices are computers → ❌ Reversal; invalid.

  4. Final Answer:

    Only Conclusion I follows → Option A

  5. Quick Check:

    Laptop chain: Laptop → Computer → Electronic ✅
Hint: Follow the arrow direction - from subset to superset only.
Common Mistakes: Reversing the direction in chain-based logic.

Mock Test

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