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Inference from Conditional Chain

Introduction

यह pattern उन questions पर केंद्रित होता है जहाँ कई conditional (“If-Then”) statements आपस में जुड़कर एक logical chain बनाते हैं। यहाँ मुख्य skill यह है कि conditions को step-by-step जोड़कर एक सही final inference निकाला जाए।

ऐसे questions analytical reasoning और logical deduction sections में आम होते हैं, जहाँ आपकी ability को test किया जाता है कि आप implications की chain को कितनी सही तरह से follow कर सकते हैं।

Pattern: Inference from Conditional Chain

Pattern

जब कई ‘If-Then’ statements आपस में जुड़ते हैं, तो एक condition का true होना आगे कई consequences को trigger कर सकता है।

Example Structure:
If A → B, and B → C, then logically A → C.

यह validity सिर्फ forward direction में ही रहती है - अगर initial condition true है, तो उसके बाद की सभी linked effects follow करेंगे।

Step-by-Step Example

Question

Statements:
1️⃣ अगर बारिश होती है, तो ज़मीन गीली हो जाती है।
2️⃣ अगर ज़मीन गीली हो जाती है, तो football match postpone हो जाएगा।
3️⃣ बारिश शुरू हो गई है।

निम्नलिखित में से कौन-सा conclusion निश्चित रूप से follow करता है?
(A) मैच postpone होगा।
(B) ज़मीन गीली नहीं होगी।
(C) मैच समय पर शुरू होगा।
(D) कुछ भी conclude नहीं किया जा सकता।

Solution

  1. Step 1: Chain पहचानें

    Rains → Ground Wet → Match Postponed.
  2. Step 2: दिए गए condition को apply करें

    बारिश शुरू ⇒ ज़मीन गीली ⇒ मैच postpone.
  3. Step 3: Options verify करें

    सिर्फ Option A सीधे conditional chain से follow करता है।
  4. Final Answer:

    मैच postpone होगा → Option A
  5. Quick Check:

    If P → Q → R और P true ⇒ R true ✅

Quick Variations

  • 1. 3-5 conditions वाले multi-step chains (If A → B, B → C, C → D...)
  • 2. Reverse inference traps (“If D → C” का मतलब “A → D” नहीं होता)
  • 3. False condition inputs (जब पहला premise false हो, तो कोई conclusion नहीं निकाला जा सकता)
  • 4. Nested या double-condition problems (“If A and B → C”)

Trick to Always Use

  • सभी statements को shared terms की मदद से जोड़कर एक clear logical chain बनाएं।
  • हमेशा given true condition से आगे बढ़ें, कभी पीछे नहीं।
  • अगर first condition false है, तो आगे के steps के बारे में कोई conclusion नहीं निकाला जा सकता।
  • Negation logic को reverse करता है: (If P → Q) का contrapositive है (If not Q → not P).

Summary

Summary

  • सभी ‘If-Then’ statements को एक linear chain में जोड़ें।
  • अगर starting condition true है, तो उसके बाद की सारी outcomes true होंगी।
  • अगर starting condition false है, तो कुछ भी definite conclude नहीं किया जा सकता।
  • हमेशा reasoning की direction test करें - सिर्फ forward, backward नहीं।

याद रखने वाला Example:
If A → B, B → C, और A true है ⇒ C true होगा ✅

Practice

(1/5)
1. Statements:<br>1️⃣ If the machine is on, the lights will glow.<br>2️⃣ If the lights glow, the room will be visible.<br>3️⃣ The machine is on.<br><br>Which of the following conclusions definitely follows?<br>(A) The lights are off.<br>(B) The room will be visible.<br>(C) The room will remain dark.<br>(D) The lights will not glow.
easy
A. The lights are off.
B. The room will be visible.
C. The room will remain dark.
D. The lights will not glow.

Solution

  1. Step 1: Identify chain

    Machine On → Lights Glow → Room Visible.
  2. Step 2: Apply given fact

    Machine is on ⇒ Lights glow ⇒ Room visible.
  3. Final Answer:

    The room will be visible → Option B
  4. Quick Check:

    P → Q → R; P true ⇒ R true ✅
Hint: If first condition is true, carry the chain forward logically.
Common Mistakes: Stopping after one inference instead of completing the chain.
2. Statements:<br>1️⃣ If it rains, the road becomes slippery.<br>2️⃣ If the road is slippery, accidents increase.<br>3️⃣ It has started raining.<br><br>Which of the following conclusions definitely follows?<br>(A) Accidents may increase.<br>(B) The road will remain dry.<br>(C) The road will be closed.<br>(D) Accidents will decrease.
easy
A. Accidents may increase.
B. The road will remain dry.
C. The road will be closed.
D. Accidents will decrease.

Solution

  1. Step 1: Chain logic

    Rain → Slippery → Accidents increase.
  2. Step 2: Given fact

    Rain started ⇒ both consequences follow.
  3. Final Answer:

    Accidents may increase → Option A
  4. Quick Check:

    Rain triggers the entire chain ✅
Hint: From a true starting event, carry to the final consequence.
Common Mistakes: Ignoring transitive middle link (slippery road).
3. Statements:<br>1️⃣ If a student studies well, they will pass the exam.<br>2️⃣ If they pass the exam, they will get a certificate.<br>3️⃣ Riya has studied well.<br><br>Which of the following conclusions definitely follows?<br>(A) Riya will get a certificate.<br>(B) Riya will fail the exam.<br>(C) Riya will not get a certificate.<br>(D) Riya did not study well.
easy
A. Riya will get a certificate.
B. Riya will fail the exam.
C. Riya will not get a certificate.
D. Riya did not study well.

Solution

  1. Step 1: Build chain

    Studies well → Pass Exam → Get Certificate.
  2. Step 2: Given

    Riya studied well ⇒ Passes exam ⇒ Gets certificate.
  3. Final Answer:

    Riya will get a certificate → Option A
  4. Quick Check:

    P → Q → R; P true ⇒ R true ✅
Hint: When the first condition is true, all following effects occur.
Common Mistakes: Assuming uncertainty when all links are definite.
4. Statements:<br>1️⃣ If electricity fails, the alarm will stop.<br>2️⃣ If the alarm stops, the guard will check the system.<br>3️⃣ Electricity has failed.<br><br>Which of the following conclusions definitely follows?<br>(A) The alarm will stop.<br>(B) The guard will check the system.<br>(C) Both A and B follow.<br>(D) The alarm will ring continuously.
medium
A. The alarm will stop.
B. The guard will check the system.
C. Both A and B follow.
D. The alarm will ring continuously.

Solution

  1. Step 1: Build chain

    Electricity fails → Alarm stops → Guard checks system.
  2. Step 2: Apply fact

    Electricity failed ⇒ both events occur.
  3. Final Answer:

    Both A and B follow → Option C
  4. Quick Check:

    Two-step logical chain ✅
Hint: When multiple consequences follow, mark both if chain is complete.
Common Mistakes: Stopping at first effect (alarm stop) only.
5. Statements:<br>1️⃣ If a country increases exports, its income rises.<br>2️⃣ If income rises, living standards improve.<br>3️⃣ Exports have increased.<br><br>Which of the following conclusions definitely follows?<br>(A) The country’s living standards will improve.<br>(B) The country’s income will fall.<br>(C) The living standards will decline.<br>(D) No definite conclusion can be drawn.
medium
A. The country’s living standards will improve.
B. The country’s income will fall.
C. The living standards will decline.
D. No definite conclusion can be drawn.

Solution

  1. Step 1: Link

    Increase Exports → Income Rises → Living Standards Improve.
  2. Step 2: Given fact

    Exports increased ⇒ Income rises ⇒ Living standards improve.
  3. Final Answer:

    The country’s living standards will improve → Option A
  4. Quick Check:

    P → Q → R; P true ⇒ R true ✅
Hint: From first true cause, every next effect in the chain must hold.
Common Mistakes: Confusing correlation with conditional certainty.

Mock Test

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