Syllogism

1. What is Syllogism?

Syllogism is a logical reasoning concept that involves drawing conclusions from given statements or premises. It tests your ability to determine what logically follows from the given information using deductive reasoning.

Deductive Reasoning

Logical Conclusions

Venn Diagram Analysis

Statement Analysis

Simple Definition: Syllogism is the process of drawing logical conclusions from given statements using deductive reasoning.

2. Types of Syllogism

Major Categories of Syllogism

Based on Approach

Statements & Conclusions

Drawing conclusions from statements

Venn Diagram Approach

Visual representation method

Logical Deduction

Pure logical reasoning

Based on Statements

Categorical Propositions

All, Some, No statements

Conditional Statements

If-Then type statements

Multiple Premises

Three or more statements

3. Statements & Conclusions

Types of Statements

Universal Positive

All A are B

Universal Negative

No A is B

Particular Positive

Some A are B

Particular Negative

Some A are not B

Statement & Conclusion Examples

Statements	Conclusion	Validity	Explanation
All cats are animals. All animals are mammals.	All cats are mammals.	Valid	Follows logically from given statements
Some birds can fly. All sparrows are birds.	Some sparrows can fly.	Invalid	"Some" doesn't guarantee all subsets
No fish can fly. All sharks are fish.	No sharks can fly.	Valid	Negative statement applies to subsets
Some apples are red. All red things are fruits.	Some apples are fruits.	Valid	Overlap between categories exists

4. Venn Diagram Approach

Venn Diagram Representations

All A are B

A inside B

No A is B

Separate circles

Some A are B

Overlapping circles

Some A not B

Partial overlap

Venn Diagram Examples

Statement Type	Venn Diagram	Possible Cases	Key Points
All A are B	A inside B	A ⊂ B	Every A is B, but B may have more elements
No A is B	Separate circles	A ∩ B = ∅	No common elements between A and B
Some A are B	Overlapping circles	A ∩ B ≠ ∅	At least one common element exists
Some A are not B	Partial A outside B	A - B ≠ ∅	At least one A that is not B

5. Rules of Syllogism

Important Rules and Principles

1

Middle Term Elimination

The middle term must be distributed at least once

2

No Negative Conclusion

If both premises are affirmative, conclusion must be affirmative

3

Particular Conclusion

If one premise is particular, conclusion must be particular

4

Universal Conclusion

If both premises are universal, conclusion can be universal

Common Syllogism Patterns

Pattern	Premise 1	Premise 2	Valid Conclusion
AAA-1	All M are P	All S are M	All S are P
EAE-1	No M are P	All S are M	No S are P
AII-1	All M are P	Some S are M	Some S are P
EIO-1	No M are P	Some S are M	Some S are not P

6. How to Solve Syllogism Questions

Step-by-Step Approach:

1

Identify Statement Types

Categorize as Universal/Particular, Positive/Negative

2

Draw Venn Diagrams

Create visual representations for each statement

3

Check All Possibilities

Consider all possible cases for "some" statements

4

Verify Conclusions

Test each conclusion against the diagrams

Remember: For "some" statements, always check all possible cases - the conclusion must be true in all possible scenarios!

7. Common Mistakes to Avoid

Frequent Errors in Syllogism

Logical Errors

Assuming "Some" means "All"

Some A are B doesn't mean All A are B

Reverse Conclusion

All A are B doesn't mean All B are A

Negative Assumption

Some A are not B doesn't mean No A are B

Diagram Errors

Wrong Overlap

Incorrect Venn diagram representation

Missing Cases

Not considering all possibilities for "some"

Overlapping Errors

Incorrect interpretation of overlapping regions

8. Common Delhi Police / SSC Exam Facts

2-Statement Syllogism → Most Common

Venn Diagram Method → Recommended

Time Limit → 60-90 seconds per question

"Some" Statements → Most Tricky

Practice → Essential for Accuracy

3-Statement Problems → Higher Difficulty

9. Quick Recap

Topic	Key Focus	Important Points
Statements & Conclusions	Logical Deduction	Universal/Positive, Universal/Negative, Particular/Positive, Particular/Negative
Venn Diagram Approach	Visual Representation	Circles for categories, Overlaps for relationships
Rules of Syllogism	Logical Principles	Middle term elimination, No negative conclusion from affirmative premises
Common Patterns	Standard Formats	AAA-1, EAE-1, AII-1, EIO-1 patterns

You've completed Syllogism!

Courage Tip: Remember that "some" means "at least one" but not necessarily "all", always draw Venn diagrams for complex problems, and practice different types of syllogism questions to master logical deduction for exams.