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Conditional “If–Then” Deduction

Introduction

Conditional reasoning उन statements पर आधारित होता है जो “If P, then Q” संरचना का उपयोग करते हैं। ऐसे statements में एक event (condition) दूसरे event (result) को logically guarantee करता है।

यह pattern aptitude और reasoning tests में अक्सर पूछा जाता है ताकि आपकी यह क्षमता जांची जा सके कि आप दिए गए conditional premises से valid consequences निकाल सकते हैं या नहीं।

Pattern: Conditional “If–Then” Deduction

Pattern

यदि statement कहता है “If P, then Q”, और P सत्य है, तो Q अवश्य सत्य होगा।

Symbolic form: If P → Q and P is true, then Q must be true। लेकिन ध्यान रहे: Q true होने पर भी यह जरूरी नहीं कि P true हो - यह एक common reasoning trap है।

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.

Options:
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: Condition और result पहचानें

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

  2. Step 2: Given fact लागू करें

    “It is raining” → P true है।

  3. Step 3: Rule लागू करें

    P → Q, और P true ⇒ Q true। इसलिए “The ground is wet” logically follow करता है।

  4. Step 4: Conclusions evaluate करें

    I. The ground is wet → ✅ Follows।
    II. It is not raining → ❌ Given fact के विपरीत।

  5. Final Answer:

    Only Conclusion I follows → Option A

  6. Quick Check:

    P true ⇒ Q true हमेशा valid।

Quick Variations

1. If P → Q और Q false ⇒ P भी false।

2. If P → Q और P false ⇒ Q के बारे में कुछ निश्चित नहीं कहा जा सकता।

3. Chain conditionals: If P → Q और Q → R ⇒ P → R।

4. Negation traps: “If not P, then not Q” अक्सर confuse करते हैं - इन्हें सावधानी से interpret करें।

Trick to Always Use

  • Step 1: Condition (P) और Result (Q) clearly identify करें।
  • Step 2: यदि P true है, तो Q अवश्य true होगा।
  • Step 3: Reverse inference (Q true ⇒ P true) कभी valid नहीं होता जब तक explicitly stated न हो।

Summary

Summary

  • “If P, then Q” का मतलब Q, P पर depend करता है; उल्टा dependency implied नहीं है।
  • P true ⇒ Q true; Q false ⇒ P false।
  • Converse (Q → P) logically invalid होता है।
  • Conditional logic में direction और dependency सबसे महत्वपूर्ण हैं।

Example to remember:
Statement: If you study, you pass the test।
Conclusion: You passed ⇒ You studied ❌ केवल “You studied ⇒ You passed” valid है।

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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