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?