Quick Rules & the Either-Or Trick

🎯 Learning Objective

Use ready-made combination rules and spot Either-Or (complementary pair) cases to answer in seconds.

💡 Concept

• All + All = All (All A are B, All B are C → All A are C)
• All + No = No (All A are B, No B is C → No A is C)
• Some + All = Some (Some A are B, All B are C → Some A are C)
• Some + No = Some-not (Some A are B, No B is C → Some A are not C)
• Two particular statements (Some / Some-not) together → NO definite conclusion
• Two negative statements together → NO definite conclusion
• Either-Or rule: if neither conclusion follows alone BUT the two are a complementary pair, answer 'Either I or II follows'
• Complementary pairs: (Some A are C) & (No A is C); or (All A are C) & (Some A are not C)

🧮 Key Formulas

All+All=All | All+No=No | Some+All=Some | Some+No=Some-not

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Two particular or two negative statements → no definite conclusion

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Complementary pair + neither alone follows → Either-Or

✏️ Easy Example

Q. Statements: All roses are red. No red is blue. Conclusion: No rose is blue. Does it follow?

1. This is the All + No = No pattern (middle term = red)
2. Roses sit inside red, and red is fully separate from blue
3. So roses are separate from blue → 'No rose is blue' follows

Answer: Yes, it follows

🇮🇳 Real-Life Example

Filling an OMR fast: once you memorise these four combos, half the syllogism set is answered on sight — leaving your time for the tricky Either-Or ones.

📝 Exam-Level Example

Q. Statements: Some books are pens. No pen is red. Conclusion: Some books are not red. Does it follow?

1. Some books are pens, and those pens are not red (No pen is red)
2. So at least those book-pens are books that are not red
3. This is the Some + No = Some-not pattern → 'Some books are not red' follows

Answer: Yes, it follows

📝 Exam-Level Example

Q. Statements: Some P are Q. Some Q are R. Conclusions: I. Some P are R. II. No P is R. Which follow?

1. Two 'Some' statements → no definite conclusion, so neither I nor II follows on its own
2. But 'Some P are R' (I) and 'No P is R' (II) are a complementary pair — in any diagram exactly one is true
3. So together they cover all cases → the answer is Either I or II follows

Answer: Either I or II follows

🪄 Memory Trick

See two 'Some' statements or two negatives? A definite conclusion is almost never there — immediately check whether the two conclusions form a complementary pair for an Either-Or answer.

⚠️ Common Mistakes

• ❌ Forcing a definite conclusion from two particular or two negative statements
• ❌ Missing an Either-Or when both conclusions are a complementary pair
• ❌ Applying a combo rule when the middle term is not shared correctly

🏆 Exam Tips

• ✅ Memorise the four combos cold — they clear half the questions instantly
• ✅ For Either-Or, both conclusions must have the SAME subject and predicate, one positive and one negative

📌 Summary

• All+All=All, All+No=No, Some+All=Some, Some+No=Some-not
• Two particular / two negative → no definite conclusion
• Either-Or = neither alone follows + complementary pair
• Complementary: (Some A are C) with (No A is C)