Syllogism Master - Quick Revision
Syllogism Master - Quick Revision
One-Liners
- All A are B ≠ All B are A.
- Some A are B = Some B are A.
- No A are B = No B are A.
- “Only A are B” ⇒ All B are A.
- Conclusion must be 100 % true; 99 % = invalid.
- Two negatives ⇒ no conclusion.
- Two particular (Some) ⇒ no conclusion.
- All + All ⇒ All.
- All + No ⇒ No.
- All + Some ⇒ no conclusion.
- Some + No ⇒ Some-not.
- Possibility is valid only when no definite exists.
- Complementary pairs: Some-not + All = at least one true.
- Venn draw smallest circle to the left.
- Shading = empty region, ‘x’ = at least one member.
- Chain rule: A→B→C ⇒ A→C.
- Conversion table: All→Some, Some→Some, No→No.
- “At least” = Some.
- “Most” = Some.
- Always check for hidden ‘Only’ & ‘Only a few’ traps.
Formulas/Rules
| Formula | Use |
|---|---|
| All A are B | Universal affirmative; convert to Some B are A |
| No A are B | Universal negative; directly convertible |
| Some A are B | Particular affirmative; reversible |
| Some A are not B | Particular negative; CANNOT convert |
| A→B + B→C ⇒ A→C | Transitive rule (chain syllogism) |
| All + Some = No conclusion | Definite conclusion blocked |
| No + Some = Some-not (reversed) | Derive complementary pair |
| Only A are B | Rewrite as All B are A |
| Possibility conclusion | Draw when no definite contradiction |
| 2 negatives (No + No) | Never give a conclusion |
Memory Tricks
- Venn Vertices: Always draw circles left-to-right → A, B, C.
- “No-Nonsense Negatives”: Two ‘No’ statements—drop them fast.
- “All-igators”: All → All keeps mouth open (transitive).
- “Some-Some Sum”: Some+Some = zero sum (no conclusion).
- “Only Owl”: Only reverses arrow—Owl looks backward.
Common Errors
| Error | Correct |
|---|---|
| Treating “Some-not” as convertible | It is NOT reversible |
| Assuming “possibility” = definite | Mark only when 100 % sure |
| Forgetting complementary pairs | One must be true in POE |
| Shading the wrong zone in Venn | Shade only the “No” area |
| Ignoring hidden “Only” | Rewrite rule before solving |
5 Quick MCQs
Show Questions
Q1. Statements: All chairs are tables. Some tables are desks.
Conclusion: I. Some desks are chairs. II. All desks are chairs.
A) Only I B) Only II C) Both D) Neither
Ans: D) Neither
Q2. Statements: No pen is pencil. Some pencils are erasers.
Conclusion: I. Some erasers are not pens. II. No eraser is pen.
A) Only I B) Only II C) Both D) Neither
Ans: A) Only I
Q3. Statements: Only boys are students. Some students are clever.
Conclusion: I. Some boys are clever. II. Some clever are boys.
A) Only I B) Only II C) Both D) Neither
Ans: C) Both
Q4. Statements: All A are B. All B are C.
Conclusion: I. All A are C. II. Some C are A.
A) Only I B) Only II C) Both D) Neither
Ans: C) Both
Q5. Statements: Some books are not pages. All pages are white.
Conclusion: I. Some books are white. II. Some white are not books.
A) Only I B) Only II C) Both D) Neither
Ans: D) Neither
BETA
