🔍 Syllogisms – Logical Reasoning
✅ What is a Syllogism?
A syllogism is a form of logical argument that applies deductive
reasoning to arrive at a conclusion based on two or more given
statements (called premises).
It typically consists of:
- • Statements – Assumed to be true.
- • Conclusions – To be verified based on the statements.
🎯 Why Learn Syllogisms?
- • Enhances deductive reasoning
- • Tests ability to connect ideas logically
- • Common in aptitude and reasoning sections of exams
🧩 Format of a Syllogism Question
Example:
• Statements:
All cats are animals.
Some animals are dogs.
• Conclusions:
I. Some dogs are cats.
II. Some animals are cats.
👉 Which conclusions follow?
🔡 Types of Statements in Syllogisms
| Statement Type | Format Example | Meaning |
|---|---|---|
| A-type (Universal Positive) | All A are B | Every A is a B |
| E-type (Universal Negative) | No A is B | No A belongs to B |
| I-type (Particular Positive) | Some A are B | At least one A is B |
| O-type (Particular Negative) | Some A are not B | At least one A is not B |
🎓 Important Concepts
🔹 1. Universal & Particular Statements
| Type | Coverage |
|---|---|
| "All A are B" | Universal Positive |
| "Some A are B" | Particular Positive |
| "No A is B" | Universal Negative |
| "Some A are not B" | Particular Negative |
🔹 2. Venn Diagrams
Used to visually represent statements and deduce correct
conclusions.
Let’s understand some examples:
✅ Case 1: All A are B
[A] inside [B]
✔ All A are B
❌ All B are A (Not necessarily)
✅ Case 2: Some A are B
[A] and [B] overlap partially
✔ Some A are B
✔ Some B are A
❌ All A are B (Not known)
✅ Case 3: No A is B
[A] and [B] are separate
✔ No A is B
✔ No B is A
💡 Rules to Remember
| Rule | Explanation |
|---|---|
| No conclusion from two particular statements | e.g. "Some A are B" + "Some B are C" = no definite conclusion |
| At least one statement must be universal | To draw a valid conclusion |
| "Some" means at least one | Could be all, but not definitely |
| Conclusion must be true in all possible cases | Even one counterexample invalidates it |
🔍 Solved Example
Q1:
• Statements:
All apples are fruits.
All fruits are tasty.
• Conclusions:
I. All apples are tasty.
II. Some tasty things are fruits.
✅ Solution:
All apples → fruits → tasty → So, I follows.
All fruits are tasty ⇒ Some tasty things are fruits – True
✅ Answer: Both I and II follow
❌ Common Mistakes
| Mistake | Correct Understanding |
|---|---|
| Assuming converse is always true | "All A are B" ≠ "All B are A" |
| Assuming possibility as certainty | “Some A are B” does not mean “All A are B” |
| Not using Venn diagrams | Visuals help spot contradictions |
🧠 Approach to Solve Syllogisms
✍ Step-by-step:
- • Read each statement carefully.
- • Identify the type (All, Some, No).
- • Draw Venn diagrams to represent sets.
- • Test each conclusion separately.
- • Use elimination for false conclusions.
🔢 Practice Questions
Q2:
• Statements:
Some pens are papers.
All papers are books.
• Conclusions:
I. Some books are pens.
II. All pens are books.
✅ Answer:
Only I is possible, but not definite.
No definite conclusion follows.
Q3:
• Statements:
All roses are flowers.
No flower is red.
• Conclusions:
I. No rose is red.
II. All flowers are roses.
✅ Answer:
Only I follows (Rose ⊆ Flowers, and no flower is red ⇒ no rose
is red)
⚠️ Important Keywords
| Word | Meaning |
|---|---|
| All | 100% of the group |
| Some | At least 1, up to all |
| No | 0% of the group |
| Some not | At least one is not |
🧠 Shortcuts (for advanced learners)
| Statement Pair | Valid Conclusion |
|---|---|
| All A are B + All B are C | ⇒ All A are C |
| All A are B + No B is C | ⇒ No A is C |
| Some A are B + All B are C | ⇒ Some A are C (Possibility only) |