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Only If / Unless Deduction

Introduction

Logical reasoning இல், “only if” மற்றும் “unless” போன்ற சொற்கள் சிறப்பு conditional தொடர்புகளை குறிக்கின்றன. ஒரு முடிவு உண்மையாக இருக்க, ஒரு condition necessary ஆ அல்லது sufficient ஆ என்பதை இவை கண்டறிய உதவுகின்றன.

இந்த அமைப்புகளைப் புரிந்துகொள்வது மிகவும் முக்கியம்; ஏனெனில் exams-ல், conditional deduction பற்றிய conceptual clarity-ஐ சோதிக்க இந்த phrases-ஐ அடிக்கடி திருப்பி வைக்கிறார்கள்.

Pattern: Only If / Unless Deduction

Pattern

“Only if” என்பது ஒரு necessary condition ஐ அறிமுகப்படுத்துகிறது.
“Unless” என்பதன் அர்த்தம் ‘if not’ அல்லது ஒரு exception condition ஐ குறிக்கிறது.

Example transformations:
- “You can enter only if you have an ID card” → If you enter, you must have an ID.
- “You will fail unless you study” → If you don’t study, you will fail. (Note: இதனால் படித்தால் கண்டிப்பாக fail ஆக மாட்டீர்கள் என்று logical-ஆக சொல்ல முடியாது.)

Step-by-Step Example

Question

Statement: “You can enter the examination hall only if you show your admit card.” கீழ்கண்டவற்றில் எது சரியானது?

(A) If you have an admit card, you can enter.
(B) If you enter, you must have an admit card.
(C) If you don’t have an admit card, you can still enter.
(D) Having an admit card is a sufficient condition to enter.

Solution

  1. Step 1: Identify key phrase

    “Only if” என்பது ஒரு necessary condition என்பதை குறிக்கிறது.

  2. Step 2: Translate logically

    “You can enter” → Entry (E); “Show admit card” → Admit (A). ஆகவே, E → A (நீங்கள் உள்ளே சென்றால், admit card இருக்க வேண்டும்).

  3. Step 3: Evaluate options

    (A) reverse relation (A → E) - ❌ உறுதி இல்லை.
    (B) சரியாக E → A என கூறுகிறது - ✅.
    (C) statement-க்கு முரண்படுகிறது - ❌.
    (D) தவறு - “only if” necessary condition கொடுக்கும்; sufficient அல்ல - ❌.

  4. Final Answer:

    If you enter, you must have an admit card → Option B

  5. Quick Check:

    “Only if” வந்தால், இரண்டாவது clause-ஐ necessary ஆக மாற்ற direction எப்போதும் flip ஆகும் ✅

Quick Variations

1. “You will pass only if you work hard” → Pass → Work Hard.

2. “You will not succeed unless you plan properly” → If not Plan → not Succeed → If Plan → Succeed.

3. “You can leave only if the manager approves” → Leave → Approval.

Trick to Always Use

  • Step 1: Keywords-ஐ அடையாளம் காணுங்கள்: “only if” → necessary; “if” → sufficient; “unless” → “if not”.
  • Step 2: Symbolic logic-ஆக மாற்றுங்கள்: A → B அல்லது ¬B → ¬A.
  • Step 3: Direction சரியா என மறுபடியும் சொல்லிப் பாருங்கள் - “only if” direction-ஐ flip செய்யும்; “unless” condition-ஐ invert செய்யும்.

Summary

Summary

  • “Only if” என்பது necessary condition-ஐ அறிமுகப்படுத்துகிறது (X → Y என்றால், X உண்மையாவதற்கு Y கட்டாயம்).
  • “If” என்பது sufficient condition-ஐ காட்டுகிறது (X → Y என்றால், X நடந்தால் Y உறுதி).
  • “Unless” என்பதன் அர்த்தம் “if not” - negation பயன்படுத்தி conditional வடிவமாக மாற்றுங்கள்.
  • Clarity க்கு, “only if” மற்றும் “unless” ஆகியவற்றை எப்போதும் standard “if-then” வடிவில் மீள எழுதுங்கள்.

நினைவில் கொள்ள வேண்டிய உதாரணம்:
“You will pass only if you study” → If you pass, you studied. “You will fail unless you study” → If you don’t study, you fail.

Practice

(1/5)
1. Statement: You will succeed only if you work hard. Which of the following is logically correct?
easy
A. If you work hard, you will succeed.
B. If you succeed, you have worked hard.
C. If you do not work hard, you will still succeed.
D. If you are lazy, you will succeed.

Solution

  1. Step 1: Identify phrase

    “Only if” → necessary condition.

  2. Step 2: Translate

    “You will succeed (S) only if you work hard (H)” → S → H.

  3. Step 3: Evaluate options

    (A) is H → S → ❌ (reversed).
    (B) correctly represents S → H → ✅.
    (C) and (D) contradict the logic → ❌.

  4. Final Answer:

    If you succeed, you have worked hard → Option B

  5. Quick Check:

    “Only if” means success requires hard work ✅
Hint: ‘Only if’ reverses the direction - the second part becomes necessary.
Common Mistakes: Treating ‘only if’ as the same as ‘if’.
2. Statement: You will not be promoted unless you perform well. Which of the following correctly expresses this statement?
easy
A. If you are promoted, you have performed well.
B. If you perform well, you will not be promoted.
C. If you do not perform well, you will not be promoted.
D. If you are promoted, you have not performed well.

Solution

  1. Step 1: Interpret ‘unless’

    ‘Unless’ = ‘if not’ condition.

  2. Step 2: Translate

    “You will not be promoted unless you perform well” → If not perform well → not promoted.

  3. Step 3: Evaluate options

    Option C states this correctly → ✅.

  4. Final Answer:

    If you do not perform well, you will not be promoted → Option C

  5. Quick Check:

    ‘Unless’ = ‘if not’ ⇒ Option C fits perfectly ✅
Hint: Replace ‘unless’ with ‘if not’ to simplify translation.
Common Mistakes: Confusing ‘unless’ with ‘only if’.
3. Statement: You can enter the lab only if you wear safety gear. Which of the following is true?
easy
A. If you enter the lab, you have worn safety gear.
B. If you wear safety gear, you can enter the lab.
C. If you don’t wear safety gear, you can still enter.
D. If you enter the lab, you have not worn safety gear.

Solution

  1. Step 1: Identify key phrase

    ‘Only if’ = necessary condition.

  2. Step 2: Translate

    “Enter (E) only if wear gear (G)” → E → G.

  3. Step 3: Verify options

    Option A states this directly → ✅; B reverses the logic (sufficient instead of necessary) → ❌.

  4. Final Answer:

    If you enter the lab, you have worn safety gear → Option A

  5. Quick Check:

    Entry requires gear ⇒ E → G ✅
Hint: In ‘only if’ statements, flip the direction for the conditional form.
Common Mistakes: Assuming ‘if’ and ‘only if’ mean the same thing.
4. Statement: A person can vote only if they are above 18 years of age. Which of the following is logically implied?
medium
A. If a person is below 18, they cannot vote.
B. If a person votes, they are above 18.
C. If a person is above 18, they must vote.
D. If a person does not vote, they are below 18.

Solution

  1. Step 1: Identify keyword

    ‘Only if’ → necessary condition.

  2. Step 2: Express relation

    Vote (V) → Age>18 (A).

  3. Step 3: Evaluate

    Option B correctly states V → A → ✅; A is required to vote.

  4. Final Answer:

    If a person votes, they are above 18 → Option B

  5. Quick Check:

    Voting requires age>18 → necessary condition ✅
Hint: Translate ‘only if’ as ‘→’ pointing toward the condition that must hold.
Common Mistakes: Interpreting as ‘if’ (sufficient) instead of ‘only if’ (necessary).
5. Statement: You will be punished unless you apologize. Which of the following is the correct logical form?
medium
A. If you are punished, you have apologized.
B. If you don’t apologize, you will be punished.
C. If you apologize, you will be punished.
D. If you don’t apologize, you will not be punished.

Solution

  1. Step 1: Interpret ‘unless’

    ‘Unless’ = ‘if not’ → If you don’t apologize → you’ll be punished.

  2. Step 2: Evaluate options

    Option B matches exactly → ✅.

  3. Step 3: Verify others

    Options A, C, D contradict or reverse meaning → ❌.

  4. Final Answer:

    If you don’t apologize, you will be punished → Option B

  5. Quick Check:

    ‘Unless’ = ‘if not’ ⇒ Option B correct ✅
Hint: ‘Unless’ = ‘if not’. Rephrase to a standard ‘if-then’ statement.
Common Mistakes: Treating ‘unless’ as ‘only if’ or reversing its meaning.

Mock Test

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