LOGICAL REASONING by R S AGGARWAL – Logical Venn Diagram – Concept of inference and conclusion.

LOGICAL REASONING by R S AGGARWAL – Logical Venn Diagram – Concept of inference and conclusion.

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Logical Venn Diagrams – Concept of Inference and Conclusion (Based on R.S. Aggarwal’s Logical Reasoning)

1. Introduction to Logical Venn Diagrams

Logical Venn Diagrams are used to represent relationships between different sets of objects or concepts using overlapping circles. These diagrams help in solving problems related to classification, syllogism, and logical inference.

2. Key Concepts in Venn Diagrams

1. Inference:

   • An inference is a logical deduction based on the given information.
   • It must be logically derived but may not be explicitly stated in the data.
   • Example: If all cats are animals, then the inference is that some animals are cats.

2. Conclusion:

   • A conclusion is a definite statement that follows from the given premises.
   • It must be true in all cases based on the Venn Diagram.
   • Example: If all birds have wings and all parrots are birds, then the conclusion is that all parrots have wings.

3. Types of Logical Venn Diagram Problems

(i) Universal Sets (All A are B)

Example:

• Statement: All doctors are professionals.
• Diagram: A circle for “Doctors” completely inside a larger circle for “Professionals.”
• Inference: Some professionals are doctors.
• Conclusion: All doctors are professionals.

(ii) Intersection of Sets (Some A are B)

Example:

• Statement: Some teachers are musicians.
• Diagram: Two overlapping circles, one for “Teachers” and another for “Musicians.”
• Inference: Some musicians are teachers.
• Conclusion: All teachers are musicians  (Not necessarily true).

(iii) Disjoint Sets (No A is B)

Example:

• Statement: No lion is a deer.
• Diagram: Two separate, non-overlapping circles (Lion and Deer).
• Inference: A deer can never be a lion.
• Conclusion: No deer is a lion.

4. Key Rules for Inference and Conclusion

Conclusions must be 100% logically correct based on the diagram.
Inference can be a possible deduction, even if not explicitly mentioned.
Overlapping sets allow common elements, while disjoint sets don’t.
A universal statement (“All A are B”) allows definite conclusions.

5. Solving Logical Venn Diagram Questions (Step-by-Step Approach)

Read the given statement carefully.
Draw a Venn Diagram representing the relationship.
Check the possible inferences and conclusions.
Validate conclusions based on logical rules.

Would you like to try some practice questions?

Here’s a comprehensive explanation of Logical Venn Diagrams, with a focus on inference and conclusion, based on the style found in R.S. Aggarwal’s Logical Reasoning — a popular book for competitive exams like GATE, CAT, SSC, and more.

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Logical Venn Diagram – Overview

Logical Venn Diagrams are diagrammatic representations used to illustrate relationships between different sets or groups. These are often used to analyze and derive inferences from given statements.

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Key Concepts

1. Venn Diagram

• A diagram using circles to represent sets.
• The overlap between circles indicates common elements.
• The non-overlapping parts indicate distinct elements.

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Types of Set Relationships

Relationship	Venn Diagram Description
All A are B	A circle inside B
Some A are B	A and B partially overlap
No A is B	A and B do not touch
Some A are not B	A and B overlap partially, some part of A is outside B

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Example Statements and Venn Diagrams

Example 1:

Statement: All dogs are animals.
Diagram:

Dog (small circle) inside Animal (big circle)

Inference: Every dog is an animal.
Conclusion: No animal is not a dog → (invalid, because some animals may not be dogs)

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Example 2:

Statement: Some cats are black.
Diagram:

Cat and Black partially overlapping circles

Inference:

• Some cats are black → (valid)
• All cats are black → (not necessarily true)
• Some black things are cats → (valid reverse possibility)

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Inference vs Conclusion

Term	Meaning
Inference	A logical result derived from one or more given premises.
Conclusion	A final statement that logically follows from the given information, which may or may not be explicitly stated.

Rules to Remember:

• An inference must be logically consistent with the Venn diagram.
• A conclusion is valid only if it holds in all possible diagrams that satisfy the given statements.

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Common Venn Diagram Questions

Question Example:
Statements:

1. All apples are fruits.
2. Some fruits are sweet.

Which of the following conclusions follow?

• A. All apples are sweet.
• B. Some fruits are apples.
• C. Some sweet things are fruits.

Answer:

• A → (not necessarily true)
• B → (all apples are fruits, so some fruits are apples)
• C → (some fruits are sweet)

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Strategy for Solving Venn Diagram Questions

1. Translate each statement into a Venn diagram.
2. Identify overlaps and exclusions.
3. Test each conclusion against the diagram.
4. Reject conclusions that are not valid in all cases.
5. Be careful with terms like “some”, “all”, “no” — they determine diagram shapes.

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Shortcut Tips from R.S. Aggarwal’s Style

• “All A are B” → Place A inside B.
• “Some A are B” → Overlapping circles.
• “No A is B” → Separate circles.
• To test possibility-based conclusions, draw multiple diagrams.
• Look for universal (100%) vs particular (some) statements.

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Would you like a few GATE-style practice questions based on this topic?