🧠 Syllogism - Formula Sheet

🎯 Basic Concepts

Proposition Types

Universal Affirmative (A): All A are B
Universal Negative (E): No A are B
Particular Affirmative (I): Some A are B
Particular Negative (O): Some A are not B

Standard Structure

Premise 1: General statement
Premise 2: General statement
Conclusion: Logical deduction

📊 Syllogism Rules

Rule of Universal Affirmative (A)

All A are B:
- Some A are B (always true)
- Some B are A (always true)
- No A are B (always false)
- All B are A (possible, not definite)

Rule of Universal Negative (E)

No A are B:
- No B are A (always true)
- Some A are not B (always true)
- Some B are not A (always true)
- All A are B (always false)

Rule of Particular Affirmative (I)

Some A are B:
- Some B are A (always true)
- No A are B (possible, not definite)
- All A are B (possible, not definite)

🔢 Venn Diagram Method

Basic Diagrams

All A are B:          Some A are B:          No A are B:
    B                     B                     B
  ┌───┐                ┌───┐                 ┌───┐
  │ A │                │ A │                 │ A │
  └───┘                └───┘                 └───┘

Multiple Categories

All A are B, All B are C:    Some A are B, Some B are C:
    C                           C
  ┌─────┐                    ┌─────┐
  │  B  │                    │  B  │
  │ ┌─┐ │                    │ ┌─┐ │
  │ │A│ │                    │ │A│ │
  │ └─┘ │                    │ └─┘ │
  └─────┘                    └─────┘

⚡ Conclusion Types

Definite Conclusions

Always follows from premises
Must be true in all cases
Cannot be false

Possible Conclusions

May or may not be true
Not definite
Cannot be concluded with certainty

False Conclusions

Contradicts given information
Cannot be true under any circumstance

📝 Solving Steps

Traditional Method

1. Identify premise types (A, E, I, O)
2. Apply syllogism rules
3. Check conclusion validity
4. Mark definite/possible/false

Venn Diagram Method

1. Draw Venn diagrams for premises
2. Check all possible arrangements
3. Verify conclusion in all cases
4. Mark valid/invalid conclusions

Quick Method

1. Combine statements directly
2. Look for immediate relationships
3. Check for common terms
4. Draw logical connections

🔍 Common Question Types

Two Premise Syllogism

Premise 1: All dogs are animals
Premise 2: All animals are living beings
Conclusion: All dogs are living beings ✓

Three Premise Syllogism

Premise 1: All A are B
Premise 2: All B are C
Premise 3: Some C are D
Check various conclusions

Either/Or Conclusions

When two conclusions:
- Complementary to each other
- One must be true
- Both cannot be false simultaneously

⚡ Quick Tips

Immediate Deductions

All A are B → Some A are B ✓
No A are B → Some A are not B ✓
Some A are B → Some B are A ✓

Combination Rules

A + A = A (All + All = All)
A + E = E (All + No = No)
E + A = O* (No + All = Some not)

Common Mistakes

Don't assume what's not given
Check all possible arrangements
Be careful with "some" statements
Don't convert "all" to "some" incorrectly

📚 Practice Strategy

Daily Practice

1. Practice different premise combinations
2. Master Venn diagram method
3. Learn quick deduction rules
4. Time yourself regularly

Skill Building

Logical thinking ability
Pattern recognition
Systematic analysis
Quick decision making

🔢 Sample Problems

Example 1

Premises:
1. All cats are animals
2. Some animals are pets

Conclusions:
I. Some cats are pets (Possible, not definite)
II. Some pets are cats (Possible, not definite)

Example 2

Premises:
1. No bird is mammal
2. All mammals are animals

Conclusions:
I. Some animals are not birds ✓ (Definite)
II. Some birds are not animals ✓ (Definite)

Master Syllogism - Draw diagrams, think logically! 🧠