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Either–Or Logical Conclusion

Introduction

Logical reasoning में “either-or” वाले statements ऐसे situations दिखाते हैं जहाँ दो में से सिर्फ एक possibility सच हो सकती है - दोनों एक साथ नहीं। यह pattern आपकी ability test करता है कि आप mutually exclusive और collectively exhaustive outcomes को पहचान पाते हैं या नहीं।

“Either-or” logic समझने से आप unnecessary assumptions avoid करते हैं और reasoning sets या syllogisms में correct conclusion चुन पाते हैं।

Pattern: Either–Or Logical Conclusion

Pattern

“Either-or” दो statements को ऐसे जोड़ता है कि अगर एक true है, तो दूसरा false होगा - और उल्टा भी।

Symbolically: Either A or B → (A ∨ B) and ¬(A ∧ B) यानी एक possibility ज़रूर true होगी, दोनों साथ में कभी true नहीं हो सकते।

Step-by-Step Example

Question

Statement: Either Rahul will go to Delhi or he will stay in Mumbai. Which of the following is true?

(A) Rahul दोनों cities में हो सकता है।
(B) Rahul किसी भी city में नहीं होगा।
(C) Rahul या तो Delhi में होगा या Mumbai में।
(D) Rahul एक ही दिन Delhi और Mumbai जा सकता है।

Solution

  1. Step 1: Keyword पहचानें

    “Either-or” → दो mutually exclusive possibilities।

  2. Step 2: Meaning समझें

    Rahul सिर्फ एक जगह हो सकता है - Delhi या Mumbai। दोनों नहीं, और न ही दोनों से बाहर।

  3. Step 3: Options evaluate करें

    (A) दोनों → ❌, (B) कोई नहीं → ❌, (C) Delhi या Mumbai → ✅, (D) दोनों same day → ❌

  4. Final Answer:

    Rahul या तो Delhi में होगा या Mumbai में → Option C

  5. Quick Check:

    “Either-or” ensures exactly one true, never both ✅

Quick Variations

1. Exclusive “Either-Or” → सिर्फ एक true।

2. Inclusive “Either-Or” → at least one true (usually daily language में)।

3. Logical puzzles में elimination या indirect inference check करने के लिए अक्सर “Either-Or” दिया जाता है।

Trick to Always Use

  • Step 1: देखें क्या दोनों outcomes एक साथ true नहीं हो सकते - यानी mutual exclusivity।
  • Step 2: याद रखें - “Either-Or” में दोनों statements कभी भी एक साथ true नहीं होते।
  • Step 3: इसे mentally ऐसे पढ़ें: “दो में से एक ज़रूर होगा, लेकिन दोनों नहीं।”

Summary

Summary

  • “Either-Or” दो opposite possibilities दिखाता है - एक true, एक false।
  • Symbolically: A ∨ B और साथ में ¬(A ∧ B)।
  • Reasoning में exclusivity check करने के लिए अक्सर use होता है।
  • Overlap eliminate करना ज़रूरी है - दोनों statements mutually exclusive होने चाहिए।

Example to remember:
“Either बारिश होगी या धूप” → दोनों एक ही समय पर नहीं हो सकते।

Practice

(1/5)
1. Statement: Either Neha will attend the meeting or she will work from home. Which of the following is true based on this statement?
easy
A. Neha can both attend the meeting and work from home.
B. Neha will neither attend the meeting nor work from home.
C. Neha will attend the meeting or work from home, but not both.
D. Neha must attend all meetings in person.

Solution

  1. Step 1: Identify logical form

    ‘Either-or’ means one of the two statements must be true, but not both.

  2. Step 2: Analyze

    Neha has two mutually exclusive actions - attend meeting (A) or work from home (W).

  3. Step 3: Evaluate options

    Option C captures this exclusivity correctly.

  4. Final Answer:

    Neha will attend the meeting or work from home, but not both → Option C

  5. Quick Check:

    ‘Either-or’ → exactly one true ✅
Hint: In ‘either-or’, only one can hold true - never both.
Common Mistakes: Assuming both statements can be true simultaneously.
2. Statement: Either the shop will open today or it will remain closed for renovation. Which statement logically follows?
easy
A. The shop may open and also undergo renovation.
B. The shop cannot be both open and under renovation at the same time.
C. The shop will remain permanently closed.
D. The shop will open tomorrow for sure.

Solution

  1. Step 1: Meaning of ‘either-or’

    One must be true - shop open (O) or closed for renovation (R).

  2. Step 2: Evaluate

    Both cannot occur together.

  3. Step 3: Verify

    Option B expresses this exclusivity correctly.

  4. Final Answer:

    The shop cannot be both open and under renovation at the same time → Option B

  5. Quick Check:

    Mutually exclusive situations → Option B ✅
Hint: Translate ‘either-or’ as exclusive scenarios - one true, one false.
Common Mistakes: Assuming both can occur together or none occurs.
3. Statement: Either the report is accurate or the manager has made an error. What can we conclude?
medium
A. The report may be inaccurate, and the manager is still correct.
B. If the report is accurate, the manager has not made an error.
C. Both the report is accurate and the manager has made an error.
D. Neither the report is accurate nor has the manager made an error.

Solution

  1. Step 1: Logic setup

    ‘Either report accurate (A) or manager error (E)’ → one true, one false.

  2. Step 2: Infer

    If A is true → E is false.

  3. Step 3: Match options

    Option B correctly represents this inverse relation.

  4. Final Answer:

    If the report is accurate, the manager has not made an error → Option B

  5. Quick Check:

    In ‘either-or’, one truth excludes the other ✅
Hint: In ‘either-or’, if one is true, negate the other automatically.
Common Mistakes: Thinking both could be false at once.
4. Statement: Either it will rain today or the weather forecast is wrong. Which of the following conclusions is valid?
medium
A. If it rains, the forecast is wrong.
B. If it doesn’t rain, the forecast is wrong.
C. It will neither rain nor will the forecast be wrong.
D. It will definitely rain today and the forecast will be right.

Solution

  1. Step 1: Breakdown

    ‘Either rain (R) or forecast wrong (F)’ → one true, not both.

  2. Step 2: Deduction

    If R is false (no rain) → F must be true (forecast wrong).

  3. Step 3: Option match

    Option B expresses this correctly.

  4. Final Answer:

    If it doesn’t rain, the forecast is wrong → Option B

  5. Quick Check:

    Negate one → the other must hold true ✅
Hint: In ‘either-or’, falsity of one ensures truth of the other.
Common Mistakes: Believing both could be true together.
5. Statement: Either Ravi will buy a car or he will invest in a new business. Which of the following is true?
medium
A. Ravi will buy a car and also invest in a business.
B. Ravi will do neither of the two.
C. If Ravi buys a car, he will not invest in a business.
D. If Ravi invests in a business, he will also buy a car.

Solution

  1. Step 1: Structure

    ‘Either buy car (C) or invest business (B)’ → one true, one false.

  2. Step 2: Analyze

    If C true → B false.

  3. Step 3: Match option

    Option C expresses this exclusivity correctly.

  4. Final Answer:

    If Ravi buys a car, he will not invest in a business → Option C

  5. Quick Check:

    ‘Either-or’ → truth of one excludes the other ✅
Hint: When you see ‘either-or’, negate the other when one is assumed true.
Common Mistakes: Assuming ‘either-or’ allows both choices.

Mock Test

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