Syllogism • Topic 1 of 4
Basic Syllogism (All / Some / No)
Start with the universal statements (All/No) — they fix the diagram. 'All A are B' puts A inside B; 'No A is B' keeps them apart. Then place the 'Some' overlaps. A conclusion follows only if it is forced in every arrangement.
The four building blocks
Every syllogism statement is one of just four types. Learn to draw each one instantly — the whole chapter is built on these four pictures.
How to read each one
| Statement | Meaning | Picture |
|---|---|---|
| All A are B | every A is also a B | A drawn completely inside B |
| No A is B | nothing is both A and B | two circles drawn apart |
| Some A are B | at least one A is a B | two circles that overlap |
| Some A are not B | at least one A is outside B | part of A sticks out of B |
Two conversions worth memorising
- All A are B always gives you Some B are A (if all roses are flowers, then some flowers are certainly roses).
- No A is B always gives you No B is A (separateness works both ways).
Golden rule. A conclusion follows only if it is true in every diagram you can legally draw. If you can draw even one diagram where it fails, it does not follow. Always hunt for the diagram that breaks the conclusion.
Two valid chains SSC reuses
- All A are B + All B are C ⇒ All A are C (so also Some A are C).
- All A are B + No B is C ⇒ No A is C.
✅ Solved examples
1. All cats are animals. All animals are living. Conclusion: All cats are living?
Cats ⊂ animals ⊂ living, so cats ⊂ living. Follows.
2. All pens are blue. No blue is red. Conclusion: No pen is red?
Pens ⊂ blue, and blue is separate from red, so pens are separate from red. Follows.
3. Some boys are tall. All tall are strong. Conclusion: Some boys are strong?
The tall boys are strong, so some boys are strong. Follows.
4. All roses are flowers. Conclusion: Some flowers are roses?
Conversion of "All": if all roses are flowers, those roses are flowers that are roses — so some flowers are roses. Follows.
✏️ Practice — try these, take hints as needed
1. All dogs are mammals. All mammals are animals. All dogs are animals?
Chain the subsets.
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Follows
2. No fish is bird. All sparrows are birds. No sparrow is fish?
Sparrows ⊂ birds, birds ∩ fish = empty.
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Follows
3. Some pens are red. All red are bright. Some pens are bright?
Red pens are bright.
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Follows
4. All A are B. Some B are A?
Conversion of All.
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Follows
5. Some A are B. Conclusion: All A are B?
Does "some" force "all"?
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Does not follow
📝 Topic test — 8 questions
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Formula Reference Sheet
This chapter
The four statement types
| All A are B | A circle sits fully inside B |
|---|---|
| No A is B | A and B circles are separate |
| Some A are B | A and B circles overlap |
| Some A are not B | part of A lies outside B |
| Golden rule | true only if it holds in EVERY valid diagram |
SSC reference
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