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Either–Or Type Syllogism

Introduction

Either-Or Type Syllogism reasoning का एक ऐसा पैटर्न है जो काफी logical और tricky माना जाता है। यह आपकी क्षमता को परखता है कि आप कब दो conclusions को mutually exclusive लेकिन collectively exhaustive समझ सकते हैं - यानी दोनों एक साथ true नहीं हो सकते, लेकिन logically इनमे से एक जरूर true होगा।

यह प्रकार banking, SSC, insurance जैसे competitive exams में बहुत आता है। इसकी logical structure समझने से “contradiction” और “complementary conclusions” में भ्रम नहीं होता।

Pattern: Either–Or Type Syllogism

Pattern

मुख्य अवधारणा: “Either-Or” pair तभी बनता है जब दोनों conclusions individually false हों, लेकिन logically इनमे से एक जरूर true होना चाहिए।

Either-Or pair बनाने की typical conditions:

  • दोनों conclusions का subject और predicate समान हो।
  • एक conclusion positive हो (“Some A are B”).
  • दूसरा negative हो (“Some A are not B”).
  • दोनों एक साथ true नहीं हो सकते, लेकिन logically एक होना ही चाहिए।

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: Statements को समझें

    Some Cars ↔ Bikes; No Bike ↔ Bus Cars और Buses के बीच direct relation निश्चित नहीं है।

  2. Step 2: Conclusion I test करें

    “Some cars are buses” ⇒ कोई support नहीं। ❌

  3. Step 3: Conclusion II test करें

    “Some cars are not buses” ⇒ इसे भी confirm नहीं कर सकते। ❌

  4. Step 4: Either-Or logic apply करें

    दोनों conclusions एक-दूसरे के opposite हैं - subject-predicate same, एक positive और दूसरा negative। ऐसी स्थिति में Either I or II follows बनता है। ✅

  5. Final Answer:

    Either I or II follows. → Option C

  6. Quick Check:

    Opposite pair (Some A are B vs Some A are not B) ⇒ Either-Or बनता है। ✅

Quick Variations

1. “Some A are B” vs “Some A are not B” - classic Either-Or।

2. “All A are B” vs “Some A are not B” - अगर दोनों साथ true नहीं हो सकते तो Either-Or।

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

4. यह केवल तभी लागू होता है जब subject और predicate दोनों conclusions में same हों।

Trick to Always Use

  • पहले check करें कि दोनों conclusions का subject-predicate same है या नहीं।
  • एक affirming हो और दूसरा denying - तभी Either-Or possible है।
  • दोनों साथ true नहीं हो सकते - यह मुख्य शर्त है।
  • याद रखें: दोनों false होने से Either-Or नहीं बनता - एक logically possible होना जरूरी है।

Summary

Summary

  • Either-Or pair तभी बनता है जब दोनों opposite conclusions same subject-predicate share करें।
  • एक positive, दूसरा negative - दोनों एक साथ true नहीं।
  • लेकिन logically एक न एक जरूर true होता है।
  • यह uncertain या dual logical possibilities को represent करने के लिए उपयोग होता है।

याद रखने के लिए उदाहरण:
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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