Syllogism
🔒 Log in to trackPossibility conclusions
🔒 Log in to track'X is a possibility' asks a different question: not 'is X forced?' but 'is X consistent with the statements?'. A possibility conclusion follows if you can draw even ONE diagram satisfying the statements where X also holds; it fails only when the statements make X impossible.
So 'All A being B is a possibility' usually follows unless a statement explicitly blocks it (typically a 'No' statement cutting across). Read carefully: a definite conclusion ('All A are B') needs to hold in every diagram; a possibility conclusion needs to hold in at least one.
Detailed notes
What a possibility conclusion asks
A definite conclusion says: "this must be true". A possibility conclusion says: "this can be true without breaking any statement". The question "All A being B is a possibility" is asking only whether some picture that satisfies the statements can also have A inside B. You are no longer the prosecutor hunting counter-examples — you are the defence lawyer who needs just one supporting diagram.
The one-diagram rule
- Read the possibility as a request: "may I draw A inside B (or A meeting B, etc.)?"
- Try to build that picture while keeping every statement true.
- If you succeed even once, the possibility follows. If every attempt collides with a statement, it fails.
What blocks a possibility
Almost always a No statement cutting across the terms. If some A is definitely a C, and No C is B, then putting all A inside B would force that C-member into B — a collision. The possibility dies. Two weaker blockers:
- An Only a few A are B statement forbids "All A are B", but still allows most other possibilities.
- A Some A are not B statement (given directly) also forbids All A are B, but allows A to move freely otherwise.
Anything not touching the terms of the possibility is irrelevant — a "No" about two far-away classes never blocks anything.
Definite vs possibility — the mirror pair
| Conclusion type | To prove it | To kill it |
|---|---|---|
| Definite ("follows") | must hold in every diagram | find ONE diagram that breaks it |
| Possibility | find ONE diagram that supports it | show EVERY diagram collides |
So the same sentence ("All A are B") can fail as a definite conclusion and still follow as a possibility. Statements "All keys are locks, some locks are doors": "Some keys are doors" fails (the door-lock overlap can dodge keys), but "All keys being doors is a possibility" follows (draw all keys inside the key-door overlap).
Worked examples
- Statements: Some books are novels. All novels are stories. Conclusion: All books being stories is a possibility. Draw all books inside stories (the book-novel part is fine, the rest of the books too) — nothing objects → follows.
- Statements: Some phones are cameras. No camera is a charger. Conclusion: All phones being chargers is a possibility. The phone-camera member is a camera, so it can never be a charger — the picture is impossible → does not follow.
Speed habits
- Possibility questions are usually faster than definite ones — one clever diagram ends the debate.
- If a "No" statement's two classes do not both touch your terms, ignore it and answer "follows".
- When one option says "X is a possibility" and the other is a definite claim, solve the definite one with counter-examples first; often only one survives.
Quick revision
- Possibility = consistent with the statements = one supporting diagram is enough.
- Definite = forced = must survive every diagram.
- Only a crossing "No" (or an explicit Some-not / only-a-few on the same pair) can kill a possibility.
- The shared member of a "Some" statement must obey every statement that mentions its class.
- Same pair can fail as definite and pass as possibility — read the wording carefully.
Types of questions asked
Every way this subtopic shows up in exams — how to recognise it, the formula or logic to use, and a solved example.
Type 1: Plain possibility (nothing blocks it)very common2 practice Q
'… is a possibility' wording and no No statement touching the two terms of the possibility.
- Try to draw the possibility (e.g. all A inside B) around the given statements.
- Keep every statement true — especially every Some-overlap.
- If one clean picture survives, the possibility follows.
Why it works: a possibility needs one consistent diagram, not all of them.
Example: All windows are doors. Some doors are gates. Conclusion: All gates being windows is a possibility.
Draw gates inside windows, windows inside doors, plus extra doors outside windows. Every statement holds → follows.
Type 2: Possibility blocked by a No statementvery common2 practice Q
The statements contain 'No X is Y' and the possibility would push a member of X (or of a class that must meet X) into Y.
- Trace the guaranteed member created by a Some statement.
- Ask: could that member be forced into a forbidden class if the possibility were drawn?
- If yes, the possibility is impossible; also test the partner conclusion with the counter-method.
Why it works: the shared member of a Some statement must obey every No statement that touches its class.
Example: Some phones are cameras. No camera is a charger. Conclusion: All phones being chargers is a possibility.
The phone-camera member is a camera, so it can never be a charger — all phones inside chargers is impossible. Does not follow.
Type 3: Possibility with only-a-few statementscommon2 practice Q
An 'Only a few A are B' statement plus a possibility conclusion about A, B or a third class.
- Split only-a-few into Some + Some-not.
- 'All A being B' is now impossible — the guaranteed non-B part forbids it.
- Other possibilities (about third classes, or All B being A) are usually still alive — try to draw them.
Why it works: only-a-few pins the A-side split; everything not touching that split stays free.
Example: Only a few chairs are sofas. All sofas are furniture. Conclusions: I. All chairs being furniture is a possibility. II. Some chairs are not sofas.
I: draw every chair inside furniture (sofa-chairs are furniture, the rest too) — nothing objects → follows. II: guaranteed by only-a-few → follows. Both follow.
Type 4: Possibility paired with a definite conclusioncommon2 practice Q
One conclusion is a possibility, the other a definite claim about the same or another pair.
- Solve the definite conclusion first with the counter-diagram method.
- Then build one diagram for the possibility.
- Match the combined result to the options — 'only I', 'only II', 'both' or 'neither'.
Why it works: the two halves use different standards (every diagram vs one diagram) and must be judged separately.
Example: All shirts are clothes. Some clothes are expensive. Conclusions: I. Some shirts are expensive. II. All expensive things being shirts is a possibility.
I: the clothes-expensive overlap can dodge shirts → fails. II: draw all expensive things inside shirts (shirts inside clothes) — consistent → follows. Only II follows.
Shortcut tricks
⚡ One supporting diagram wins for possibility
For possibility conclusions, flip your thinking: you are now the defence lawyer. Build one diagram where the possibility is true alongside all statements — done, it follows.
Example: Q. Statements: All keys are metal. Some metal is rusty. 'All rusty things being keys is a possibility' — follows?
Sol. Draw rusty ⊆ keys, keys ⊆ metal, and a second metal piece outside keys. All statements + possibility hold → follows.
Definite = survive every diagram; possibility = survive in one diagram.
Where students lose marks
Testing a possibility conclusion like a definite one (demanding it hold everywhere).
Declaring a possibility false when a 'No' statement doesn't actually touch the terms.
Practice sets — 12 questions
Sets of 10, mixed across the question types above. Each answer comes with a step-by-step explanation.
Topic test · 12 questions
Suggested time 11 min · wrong answers go to your mistake notebook automatically.