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Premise–Conclusion Single Chain

Introduction

Many logical reasoning questions are based on linked premises - where one statement connects to another to form a logical chain. The key is to trace this chain correctly and identify what conclusion follows naturally.

This pattern is important because it forms the backbone of syllogistic reasoning, helping you deduce indirect relationships using transitive logic (A → B → C ⇒ A → C).

Pattern: Premise–Conclusion Single Chain

Pattern

When two statements share a common term, combine them logically to derive a direct conclusion.

Example structure:
If “All A are B” and “All B are C”, then All A are C. This is known as the transitive deduction rule.

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.

Which of the following options is correct?

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: Understand the premises

    Premise 1: All dogs ⊂ Mammals.
    Premise 2: All mammals ⊂ Animals.

  2. Step 2: Identify the common term

    The shared term is “mammals”. Using transitive logic: if dogs are mammals, and mammals are animals → dogs are animals.

  3. Step 3: Test each conclusion

    I. All dogs are animals → ✅ Follows logically.
    II. All animals are dogs → ❌ Reverses the logic; invalid.

  4. Final Answer:

    Only Conclusion I follows → Option A

  5. Quick Check:

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

Quick Variations

1. Questions with “Some” or “No” instead of “All”.

2. Reverse-chaining where terms are inverted - check for direction consistency.

3. Chain may include more than two links (A → B → C → D).

4. Occasionally includes negatives (“No A is B”) - use logical elimination instead of transitivity.

Trick to Always Use

  • Step 1: Identify the middle term connecting both statements.
  • Step 2: Connect the first and last terms - drop the middle term.
  • Step 3: Keep direction consistent - don’t reverse the arrow of logic.

Summary

Summary

  • Premise-Conclusion chains follow transitive logic: A → B and B → C ⇒ A → C.
  • The shared (middle) term helps form a valid link between unrelated items.
  • Never reverse direction - “All A are B” ≠ “All B are A”.
  • Always check that your conclusion preserves logical direction and scope.

Example to remember:
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.

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