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Either–Or Type Syllogism

Introduction

The Either-Or Type Syllogism is one of the most logical and conceptually tricky patterns in reasoning. It tests your ability to identify mutually exclusive but collectively exhaustive conclusions - situations where one of two statements must be true, but both cannot be true simultaneously.

This type frequently appears in competitive exams such as banking, SSC, and insurance tests, and understanding its logical structure helps avoid common confusion between contradiction and complementarity.

Pattern: Either–Or Type Syllogism

Pattern

The key concept: Two conclusions form an “Either-Or” pair only when both are individually false but one of them must be true logically.

Typical conditions for forming an Either-Or pair:

  • They must have the same subject and predicate.
  • One conclusion is positive (e.g., “Some A are B”).
  • The other is negative (e.g., “Some A are not B”).
  • Both cannot be true together, but one must be true.

Step-by-Step Example

Question

Statements:
1️⃣ Some cars are bikes.
2️⃣ No bike is a bus.

Conclusions:
I. Some cars are buses.
II. Some cars are not buses.

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 given statements

    Some Cars ↔ Bikes; No Bike ↔ Bus ⇒ Cars and Buses are indirectly related, but relation is unclear.

  2. Step 2: Test Conclusion I

    “Some cars are buses” ⇒ Not supported; no link exists. ❌

  3. Step 3: Test Conclusion II

    “Some cars are not buses” ⇒ Also cannot be confirmed. ❌

  4. Step 4: Apply Either-Or logic

    Both conclusions are opposite in nature (same subject-predicate, one positive, one negative). Hence, Either I or II follows. ✅

  5. Final Answer:

    Either I or II follows. → Option C

  6. Quick Check:

    Opposite pair (Some A are B / Some A are not B) → Either-Or ✅

Quick Variations

1. “Some A are B” vs “Some A are not B” - classical Either-Or form.

2. “All A are B” vs “Some A are not B” - conditional Either-Or if both can’t be true.

3. “No A is B” vs “Some A are B” - direct contradiction leading to Either-Or.

4. Applicable only if subject and predicate are same in both conclusions.

Trick to Always Use

  • Check for same subject-predicate pair.
  • Ensure one conclusion affirms and the other denies the relation.
  • If both cannot be true together, test for “Either-Or”.
  • Remember: both being false together doesn’t trigger Either-Or - one must be logically possible.

Summary

Summary

  • Either-Or occurs when two opposite conclusions share same subject and predicate.
  • They must be contradictory (positive vs negative).
  • Both cannot be true simultaneously, but one must hold.
  • Used to cover both logical possibilities under uncertainty.

Example to remember:
Some A are B, Some A are not B ⇒ Either I or II follows ✅

Practice

(1/5)
1. Statements: 1️⃣ Some pens are pencils. 2️⃣ No pencil is eraser. Conclusions: I. Some pens are erasers. II. Some pens are not erasers.
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 the statements

    Some pens are pencils ⇒ there exists a portion of Pens that is inside Pencils. No pencil is eraser ⇒ Pencils ∩ Erasers = ∅ (pencils are completely outside erasers).

  2. Step 2: Draw the inference

    The pens that lie in the Pencil portion cannot be erasers because Pencils and Erasers are disjoint. Therefore at least some pens are definitely not erasers. ✅

  3. Step 3: Test the other conclusion

    ‘Some pens are erasers’ contradicts the given ‘No pencil is eraser’ for the pens that are pencils, and there is no information about pens outside the pencil portion to support Conclusion I. ❌

  4. Final Answer:

    Only Conclusion II follows. → Option B

  5. Quick Check:

    Some Pens ⊂ Pencils and Pencils ∩ Erasers = ∅ ⇒ those Pens ≠ Erasers → Some pens are not erasers. ✅
Hint: If Some A are B and No B is C ⇒ those Some A are not C.
Common Mistakes: Thinking 'Some' implies membership outside the intersecting subset without checking exclusions.
2. Statements: 1️⃣ All cats are animals. 2️⃣ Some animals are not dogs. Conclusions: I. Some cats are dogs. II. Some cats are not dogs.
easy
A. Either I or II follows
B. Only Conclusion II follows
C. Both I and II follow
D. Neither I nor II follows

Solution

  1. Step 1: Identify the relation

    All Cats ⊂ Animals; Some Animals are not Dogs ⇒ uncertain relation between Cats and Dogs.

  2. Step 2: Test conclusions

    ‘Some cats are dogs’ ❌ not supported, ‘Some cats are not dogs’ ❌ also not confirmed.

  3. Step 3: Apply Either-Or logic

    Same subject-predicate (Cats-Dogs) with one positive and one negative ⇒ Either-Or condition satisfied. ✅

  4. Final Answer:

    Either I or II follows. → Option A

  5. Quick Check:

    Uncertain relation + opposite conclusions = Either-Or. ✅
Hint: Uncertain relation + contradictory conclusions → Either-Or.
Common Mistakes: Assuming one definite truth.
3. Statements: 1️⃣ Some books are pages. 2️⃣ All pages are papers. Conclusions: I. Some books are papers. II. Some books are not papers.
easy
A. Neither I nor II follows
B. Only Conclusion I follows
C. Only Conclusion II follows
D. Either I or II follows

Solution

  1. Step 1: Combine statements

    Some Books ↔ Pages; All Pages ⊂ Papers ⇒ therefore, Some Books ⊂ Papers. ✅

  2. Step 2: Evaluate conclusions

    Conclusion I (‘Some books are papers’) follows logically. ✅ Conclusion II (‘Some books are not papers’) contradicts the result. ❌

  3. Final Answer:

    Only Conclusion I follows. → Option B

  4. Quick Check:

    Some + All ⇒ Some → valid conclusion. ✅
Hint: Some + All ⇒ Some.
Common Mistakes: Marking Either-Or when one conclusion is valid.
4. Statements: 1️⃣ Some fruits are mangoes. 2️⃣ All mangoes are sweet. Conclusions: I. Some fruits are not sweet. II. All sweet things are fruits.
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: Analyze premises

    Some Fruits ⊂ Mangoes; All Mangoes ⊂ Sweet ⇒ Fruits ⊂ Sweet partially, but no universal link established.

  2. Step 2: Test conclusions

    ‘Some fruits are not sweet’ ❌ contradicts given; ‘All sweet things are fruits’ ❌ goes beyond data. Neither conclusion is valid.

  3. Final Answer:

    Neither I nor II follows. → Option D

  4. Quick Check:

    If data doesn’t cover totality, avoid universal conclusions. ✅
Hint: If statements are unrelated or lack overlap, neither conclusion follows.
Common Mistakes: Applying Either-Or without opposite relation.
5. Statements: 1️⃣ Some laptops are mobiles. 2️⃣ Some mobiles are not gadgets. Conclusions: I. Some laptops are gadgets. II. Some laptops are not gadgets.
medium
A. Only Conclusion I follows
B. Either I or II follows
C. Only Conclusion II follows
D. Neither I nor II follows

Solution

  1. Step 1: Understand statements

    Some Laptops ↔ Mobiles; Some Mobiles are not Gadgets ⇒ Uncertain link between Laptops and Gadgets.

  2. Step 2: Check conclusions

    ‘Some laptops are gadgets’ ❌ not proven; ‘Some laptops are not gadgets’ ❌ also unproven individually.

  3. Step 3: Apply Either-Or condition

    Both share same subject-predicate (Laptops-Gadgets) but are opposites. Both cannot be true, one must be true. ✅

  4. Final Answer:

    Either I or II follows. → Option B

  5. Quick Check:

    ‘Some A are B’ vs ‘Some A are not B’ with uncertain relation ⇒ Either-Or applies. ✅
Hint: When two opposite conclusions (positive & negative) share same terms and data doesn’t confirm either - choose Either-Or.
Common Mistakes: Marking one conclusion as true without checking the uncertainty condition.

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