Syllogism Rules
Syllogism – 60-Second Crash Sheet
| Std. Propositions | Letter | Quantity | Quality | Distribution |
|---|---|---|---|---|
| All A are B | A | Universal | Affirm. | A only |
| No A is B | E | Universal | Neg. | Both A & B |
| Some A are B | I | Particular | Affirm. | None |
| Some A are not B | O | Particular | Neg. | B only |
1. Must-Know Rules
- A → I (All ⇒ Some) – always valid
- E → O (No ⇒ Some-not) – always valid
- I ⇄ O never converts
- Middle term must be distributed at least once
- No term in conclusion can be more widely distributed than in premise
- Two particular (I/O) premises ⇒ no definite conclusion
- Two negatives (E+E or E+O) ⇒ no definite conclusion
- A+E or E+A ⇒ universal negative conclusion (E-type)
- A+I or I+A ⇒ particular affirmative (I-type)
- I+O or O+I ⇒ no universal conclusion
2. Quick-Fire Mnemonics
- MUD: Middle term must be Universally Distributed at least once.
- PPNC: P + P ⇒ No Conclusion (two particulars).
- NNC: N + N ⇒ No Conclusion (two negatives).
- Venn-in-Head: Draw circles instantly; overlap = “Some”, separate = “No”, inside = “All”.
3. Most-Used Conclusion Table
| Premise 1 | Premise 2 | Valid Conclusion | Else |
|---|---|---|---|
| A | A | A (or I) | — |
| A | E | E | — |
| A | I | I | — |
| A | O | O | — |
| E | I | O* | — |
| I | I | — | No conclusion |
| O | O | — | No conclusion |
*Sub-alternation: E + I ⇒ O (particular negative)
4. Reverse-Pair Traps ( examiner favourites )
- “Some A are B” CANNOT give “All B are A”
- “Some A are not B” CANNOT give “Some B are not A”
- Converse of ‘A’ is ‘I’ only; Converse of ‘E’ is ‘E’ only.
Rapid-Fire MCQs
Attempt in 60 s; click to reveal answers.
BETA
