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Conditional “If–Then” Deduction

Introduction

Conditional reasoning என்பது “If P, then Q” என்ற pattern-ஐ அடிப்படையாகக் கொண்ட statements-ஐ குறிக்கிறது. இத்தகைய statements-ல், ஒரு நிகழ்வு (condition அல்லது cause) மற்றொரு நிகழ்வை (result அல்லது effect) உறுதியாக ஏற்படுத்தும் என்ற தர்க்க உறவு விளக்கப்படுகிறது.

இந்த pattern, aptitude மற்றும் reasoning tests-ல் அதிகமாக பயன்படுத்தப்படுகிறது; ஏனெனில் conditional premises-இலிருந்து valid consequences-ஐ கண்டறியவும், தவறான முடிவுகளை நிராகரிக்கவும் உங்கள் திறனை இது சோதிக்கும்.

Pattern: Conditional “If–Then” Deduction

Pattern

ஒரு statement “If P, then Q” என்று சொன்னால், P உண்மை என்றால் Q உண்மை என்று conclude செய்யலாம்.

Symbolic form-ல்: If P → Q மற்றும் P உண்மை என்றால், Q கட்டாயமாக உண்மை. ஆனால் Q உண்மை என்றால், அது P உண்மை என்பதைக் கட்டாயமாகக் குறிக்காது (இது பொதுவான reasoning trap).

Step-by-Step Example

Question

Statements:
1️⃣ If it rains, the ground becomes wet.
2️⃣ It is raining.

Conclusions:
I. The ground is wet.
II. It is not raining.

கீழ்கண்ட options-ல் எது சரியானது?

Options:
A. Conclusion I மட்டும் follows
B. Conclusion II மட்டும் follows
C. I மற்றும் II இரண்டும் follow ஆகும்
D. I மற்றும் II எதுவும் follow ஆகாது

Solution

  1. Step 1: condition மற்றும் result-ஐ அடையாளம் காணுங்கள்

    Conditional rule: If it rains (P), then ground becomes wet (Q).

  2. Step 2: கொடுக்கப்பட்ட fact-ஐ பயன்படுத்துங்கள்

    It is raining → P உண்மை.

  3. Step 3: rule logic-ஐ பயன்படுத்துங்கள்

    If P → Q, மற்றும் P உண்மை ⇒ Q கட்டாயமாக உண்மை. ஆகவே, “The ground is wet” follows.

  4. Step 4: conclusions-ஐ மதிப்பீடு செய்யுங்கள்

    I. The ground is wet → ✅ தர்க்கபூர்வமாக follows.
    II. It is not raining → ❌ கொடுக்கப்பட்ட fact-க்கு முரண்படுகிறது.

  5. Final Answer:

    Conclusion I மட்டும் follows → Option A

  6. Quick Check:

    Raining (P) ⇒ Wet ground (Q). Condition பூர்த்தியானதால் ⇒ Conclusion valid ✅

Quick Variations

1. If P → Q, மற்றும் Q பொய்யானது ⇒ P கட்டாயமாக பொய்யானது.

2. If P → Q, மற்றும் P பொய்யானது ⇒ Q பற்றி எந்த definite conclusion-உம் இல்லை.

3. Multiple chained conditionals (If P → Q, If Q → R ⇒ P → R).

4. “If not P, then not Q” போன்ற conditional negations பொதுவாக logical traps ஆக தோன்றும்.

Trick to Always Use

  • Step 1: condition (P) மற்றும் result (Q) எது என்பதை கண்டறியுங்கள்.
  • Step 2: truth logic-ஐ பயன்படுத்துங்கள் - P உண்மை என்றால் ⇒ Q உண்மை.
  • Step 3: reverse (Q → P) எப்போதும் valid அல்ல; explicit-ஆக சொல்லப்படவில்லை என்றால் ஏற்றுக்கொள்ள வேண்டாம்.

Summary

Summary

  • “If P, then Q” என்றால் Q, P-இல் சார்ந்தது - மாறாக அல்ல.
  • P உண்மை என்றால் Q கட்டாயமாக follows; Q பொய்யானால் P பொய்யானதாக இருக்க வேண்டும்.
  • converse (If Q → P) என்பது தர்க்கபூர்வமாக தவறானது; நிரூபிக்கப்படாவிட்டால் ஏற்கக் கூடாது.
  • conditional logic-ல் direction மற்றும் dependency-ஐ எப்போதும் கவனமாகச் சரிபார்க்குங்கள்.

நினைவில் வைக்க வேண்டிய example:
Statement: If you study, you pass the test.
Conclusion: You passed the test ⇒ You studied ❌ (invalid converse). “You studied ⇒ You passed” மட்டும் ✅

Practice

(1/5)
1. Statements: If the phone battery is dead, the phone will not switch on. The phone battery is dead. Conclusions: I. The phone will not switch on. II. The phone is under warranty. 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 the conditional

    If Battery Dead (P) → Phone won't switch on (Q).

  2. Step 2: Apply given fact

    Battery is dead → P is true.

  3. Step 3: Deduce

    From P → Q and P true ⇒ Q true. So the phone will not switch on. There is no information about warranty.

  4. Final Answer:

    Only Conclusion I follows → Option A

  5. Quick Check:

    Condition met (battery dead) ⇒ result (won't switch on) ✅
Hint: If P → Q and P holds, conclude Q; warranty info is unrelated.
Common Mistakes: Assuming unrelated facts (like warranty) follow from the condition.
2. Statements: If a student studies, then he will pass the exam. The student did not study. Conclusions: I. The student did not pass the exam. II. Nothing definite can be said about whether the student passed. 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 conditional

    If Studies (P) → Pass (Q).

  2. Step 2: Note given fact

    P is false (student did not study).

  3. Step 3: Apply logic

    When P is false, we cannot conclude Q is false - the conditional is a sufficient condition, not necessary. So we cannot say the student did not pass; only that no definite conclusion about passing follows.

  4. Final Answer:

    Only Conclusion II follows → Option B

  5. Quick Check:

    Not studying does not logically force failure (there may be other reasons to pass) ✅
Hint: P false ⇒ no definite inference about Q for 'If P → Q'.
Common Mistakes: Treating a sufficient condition as necessary (assuming not P ⇒ not Q).
3. Statements: If it snows, the roads become slippery. All slippery roads are dangerous. It is snowing. Conclusions: I. Roads are slippery. II. Roads are dangerous. 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: Chain the conditionals

    If Snows (P) → Roads Slippery (Q). Also All Slippery (Q) → Dangerous (R).

  2. Step 2: Apply given fact

    It is snowing → P true ⇒ Q true (roads slippery).

  3. Step 3: Transitive deduction

    Q true and Q → R ⇒ R true (roads dangerous).

  4. Final Answer:

    Both I and II follow → Option C

  5. Quick Check:

    Snow ⇒ slippery ⇒ dangerous. Both conclusions hold ✅
Hint: Chain P → Q and Q → R to get P → R when P holds.
Common Mistakes: Stopping after the first conditional and missing the transitive effect.
4. Statements: If the ignition key is turned, the engine starts. The engine has started. Conclusions: I. The key was turned. II. The car will run. 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 conditional

    If Key Turned (P) → Engine Starts (Q).

  2. Step 2: Apply given fact

    Engine has started → Q is true.

  3. Step 3: Evaluate conclusions

    I. The key was turned → ❌ Q true does not necessarily imply P true (converse is not valid).
    II. The car will run → ❌ Not guaranteed by ‘engine starts’ alone (there may be other faults). No direct rule provided that engine start ⇒ car will run.

  4. Final Answer:

    Neither I nor II follows → Option D

  5. Quick Check:

    Q true alone is insufficient to conclude P or additional effects unless explicitly stated ✅
Hint: Do not assume converse (Q → P) unless given; avoid extra unwarranted inferences.
Common Mistakes: Inferring the cause from the effect (invalid converse).
5. Statements: If you water the plant, it grows. You watered the plant. Conclusions: I. The plant will grow. II. The plant received sunlight. 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 conditional

    If Watered (P) → Plant Grows (Q).

  2. Step 2: Apply the fact

    You watered the plant → P true.

  3. Step 3: Deduce

    P true and P → Q ⇒ Q true (the plant will grow). There is no information about sunlight.

  4. Final Answer:

    Only Conclusion I follows → Option A

  5. Quick Check:

    Given sufficient condition (watering) holds, growth follows in the scope of the premise ✅
Hint: When P is given and P → Q, accept Q and avoid assuming unrelated facts.
Common Mistakes: Adding extra causes/effects not present in the premise.

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