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Deduction with Multiple Premises

Introduction

Logical reasoning में कई problems ऐसे होते हैं जहाँ आपको दो या अधिक premises को combine करके conclusion निकालना होता है। ऐसे questions आपकी ability test करते हैं कि आप statements को step-by-step logically link कर सकें और एक पूरी chain बना सकें।

यह pattern important है क्योंकि यह आपकी transitive reasoning skills को develop करता है और complex syllogisms तथा inference-based sets को solve करने में मदद करता है।

Pattern: Deduction with Multiple Premises

Pattern

मुख्य विचार यह है कि दिए गए premises (facts) को logically combine करके ऐसा conclusion निकालें जो आवश्यक रूप से follow करे - न उससे कम, न ज़्यादा।

उदाहरण: अगर A → B और B → C, तो हम valid conclusion निकाल सकते हैं: A → C. इसे Transitive Deduction कहते हैं।

Step-by-Step Example

Question

Premises:
1️⃣ All fruits are food.
2️⃣ All apples are fruits.
3️⃣ All food items are edible.

कौन-सा conclusion निश्चित रूप से follow करता है?
(A) All fruits are apples.
(B) All apples are edible.
(C) Some apples are not edible.
(D) All edible items are apples.

Solution

  1. Step 1: पहले दो premises को link करें

    All apples ⊂ fruits; All fruits ⊂ food ⇒ All apples ⊂ food.

  2. Step 2: तीसरे premise को जोड़ें

    All food ⊂ edible ⇒ All apples ⊂ edible.

  3. Step 3: बाकी options verify करें

    ‘All fruits are apples’ ❌ reverse है।
    ‘Some apples not edible’ ❌ contradict करता है।
    ‘All edible are apples’ ❌ बहुत broad है।

  4. Final Answer:

    All apples are edible → Option B

  5. Quick Check:

    Chain: Apples → Fruits → Food → Edible ✅

Quick Variations

1. तीन या अधिक premises के साथ transitive deduction।

2. Negative premises वाले chains (जैसे “No A is B, All B are C”).

3. Reverse या indirect logical links।

4. “If-then” वाली conditional chains जो कई links में फैलती हैं।

Trick to Always Use

  • Step 1: Premises को order में arrange करें (A → B → C).
  • Step 2: Common terms identify करके logical chain बनाएं।
  • Step 3: Direction check करें - chain सिर्फ forward direction में valid होती है।
  • Step 4: Reverse या unrelated statements तुरंत eliminate करें।

Summary

Summary

  • Multiple premises तभी combine होते हैं जब उनके बीच shared terms हों।
  • Transitive logic तभी काम करता है जब सभी links एक ही direction में हों।
  • Negative statements chain को तोड़ सकते हैं - ध्यान से handle करें।
  • हमेशा first subject से final object तक का logical flow maintain करें।

Example to remember:
अगर All A → B, All B → C, और All C → D ⇒ All A → D ✅

Practice

(1/5)
1. Premises:<br>1️⃣ All poets are writers.<br>2️⃣ All writers are readers.<br>3️⃣ Some readers are thinkers.<br><br>Which of the following conclusions definitely follows?<br>(A) All poets are readers.<br>(B) Some poets are thinkers.<br>(C) All thinkers are readers.<br>(D) Some writers are not poets.
easy
A. All poets are readers.
B. Some poets are thinkers.
C. All thinkers are readers.
D. Some writers are not poets.

Solution

  1. Step 1: Link Premises

    All poets ⊂ writers, and all writers ⊂ readers ⇒ All poets ⊂ readers.

  2. Step 2: Evaluate Other Options

    ‘Some poets are thinkers’ - not directly stated → Uncertain. ‘All thinkers are readers’ - not given. ‘Some writers are not poets’ - not stated.

  3. Final Answer:

    All poets are readers → Option A

  4. Quick Check:

    Poets → Writers → Readers ✅
Hint: Combine consecutive ‘All’ statements to form a clear chain.
Common Mistakes: Assuming extra links like ‘poets are thinkers’.
2. Premises:<br>1️⃣ All roses are flowers.<br>2️⃣ Some flowers are red.<br>3️⃣ All red things are attractive.<br><br>Which of the following conclusions definitely follows?<br>(A) All flowers are attractive.<br>(B) Some flowers are attractive.<br>(C) Some red things are roses.<br>(D) All red things are flowers.
easy
A. All flowers are attractive.
B. Some flowers are attractive.
C. Some red things are roses.
D. All red things are flowers.

Solution

  1. Step 1: Link Premises

    Some flowers are red; all red things are attractive ⇒ Some flowers are attractive.

  2. Step 2: Eliminate Others

    ‘All flowers are attractive’ ❌ not stated. ‘Some red things are roses’ ❌ not given. ‘All red things are flowers’ ❌ reverse.

  3. Final Answer:

    Some flowers are attractive → Option B

  4. Quick Check:

    Flowers → Red → Attractive ✅
Hint: ‘Some + All’ combination yields ‘Some’ relation at the end.
Common Mistakes: Extending ‘some’ to mean ‘all’.
3. Premises:<br>1️⃣ All students are learners.<br>2️⃣ Some learners are teachers.<br>3️⃣ All teachers are professionals.<br><br>Which of the following conclusions definitely follows?<br>(A) Some students are professionals.<br>(B) Some professionals are learners.<br>(C) All learners are professionals.<br>(D) All professionals are students.
medium
A. Some students are professionals.
B. Some professionals are learners.
C. All learners are professionals.
D. All professionals are students.

Solution

  1. Step 1: Link Premises

    Some learners ⊂ teachers; all teachers ⊂ professionals ⇒ Some learners ⊂ professionals ⇒ Some professionals ⊂ learners.

  2. Step 2: Evaluate

    ‘Some professionals are learners’ follows from reverse inclusion → ✅ True.

  3. Final Answer:

    Some professionals are learners → Option B

  4. Quick Check:

    Learners → Teachers → Professionals ✅
Hint: Reverse the ‘Some-All’ chain to get valid ‘Some’ conclusions.
Common Mistakes: Assuming ‘All learners are professionals’.
4. Premises:<br>1️⃣ All cats are animals.<br>2️⃣ No animal is a plant.<br>3️⃣ All plants are living things.<br><br>Which of the following conclusions definitely follows?<br>(A) No cat is a plant.<br>(B) Some cats are living things.<br>(C) All animals are plants.<br>(D) Some living things are animals.
medium
A. No cat is a plant.
B. Some cats are living things.
C. All animals are plants.
D. Some living things are animals.

Solution

  1. Step 1: Link First Two Premises

    All cats ⊂ animals, no animal ⊂ plant ⇒ No cat ⊂ plant.

  2. Step 2: Validate

    This follows directly and necessarily.

  3. Final Answer:

    No cat is a plant → Option A

  4. Quick Check:

    Negative premise extends across category ✅
Hint: ‘No A is B’ transfers exclusion to all subgroups.
Common Mistakes: Forgetting negative statements propagate exclusion.
5. Premises:<br>1️⃣ All engineers are logical.<br>2️⃣ Some logical people are mathematicians.<br>3️⃣ No mathematician is lazy.<br><br>Which of the following conclusions definitely follows?<br>(A) Some engineers are mathematicians.<br>(B) Some logical people are not lazy.<br>(C) All engineers are lazy.<br>(D) No logical person is an engineer.
medium
A. Some engineers are mathematicians.
B. Some logical people are not lazy.
C. All engineers are lazy.
D. No logical person is an engineer.

Solution

  1. Step 1: Combine Premises

    Some logical ⊂ mathematicians; no mathematician ⊂ lazy ⇒ Some logical ⊂ not lazy.

  2. Step 2: Evaluate Options

    ‘Some logical people are not lazy’ directly follows ⇒ ✅ True.

  3. Final Answer:

    Some logical people are not lazy → Option B

  4. Quick Check:

    Logical → Mathematician → Not Lazy ✅
Hint: When a negative appears at the end, carry exclusion backward.
Common Mistakes: Linking engineers with mathematicians unnecessarily.

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