Possibility Conclusions & Multiple Diagrams

🎯 Learning Objective

Handle 'possibility' conclusions, which need to be true in just one valid diagram, and know when a possibility is blocked.

💡 Concept

• A possibility conclusion ('Some A can be B', 'All A being B is a possibility') FOLLOWS if it is true in at least ONE valid diagram
• A definite conclusion must be true in ALL diagrams; a possibility needs only ONE — the tests are opposite
• A possibility FAILS only when it is impossible in every diagram
• If the statements force 'No overlap' (a definite No), then 'some overlap is possible' is blocked and fails
• Every 'Some' statement allows more than one diagram — draw the alternatives before deciding
• From 'Some A are B', 'All A are B' is usually a possibility unless a statement blocks it

🧮 Key Formulas

Definite conclusion → true in ALL diagrams

>

Possibility conclusion → true in AT LEAST ONE diagram

>

Forced 'No overlap' ⇒ any 'overlap possible' conclusion fails

✏️ Easy Example

Q. Statements: Some pens are books. All books are copies. Conclusion: All pens being copies is a possibility. Does it follow?

1. The pens that are books are already inside copies (All books are copies)
2. The remaining pens can be drawn inside copies too — nothing forbids it
3. So a diagram with every pen inside copies is valid → the possibility holds

Answer: Yes, it follows (it is a valid possibility)

🇮🇳 Real-Life Example

A recruiter wondering 'could every shortlisted candidate also be a topper?' isn't claiming it is certain — only checking whether it is possible. That is exactly a possibility conclusion.

📝 Exam-Level Example

Q. Statements: All cats are pets. No pet is wild. Conclusions: I. No cat is wild. II. Some cats being wild is a possibility. Which follow?

1. Cats are inside pets, and no pet touches wild → cats cannot touch wild
2. I: 'No cat is wild' is forced in every diagram → follows
3. II: since cats can NEVER be wild, 'some cats being wild' is impossible in every diagram → fails

Answer: Only conclusion I follows

📝 Exam-Level Example

Q. Statements: Some A are B. Some B are C. Conclusions: I. Some A are C. II. Some A being C is a possibility. Which follow?

1. A overlaps B, and B overlaps C, but A and C need not touch
2. I: 'Some A are C' is NOT guaranteed — a diagram exists where A and C are separate, so it does not follow
3. II: we CAN draw a diagram where A and C overlap → the possibility is valid → follows

Answer: Only conclusion II follows

🪄 Memory Trick

Read the wording first: 'definitely follows?' means test every diagram; 'is a possibility?' means you only need to draw ONE diagram where it works — unless a definite No blocks it.

⚠️ Common Mistakes

• ❌ Judging a possibility conclusion by the 'must be true always' rule
• ❌ Calling an overlap 'possible' when the statements already force No overlap
• ❌ Drawing only one diagram when a 'Some' statement allows several

🏆 Exam Tips

• ✅ For a possibility, your job is to CONSTRUCT one working diagram, not to prove it always holds
• ✅ A definite 'No' between two sets kills every 'they can overlap' possibility

📌 Summary

• Possibility follows if true in at least one diagram
• Definite = all diagrams; possibility = one diagram
• A forced 'No overlap' blocks the matching possibility
• Always sketch the alternative diagrams for 'Some' statements