How to Solve Syllogism Possibility Cases
Solve syllogism possibility questions by drawing a valid diagram consistent with all premises, with a worked example and practice questions.
Expected Interview Answer
A syllogism “possibility” question asks whether a conclusion COULD be true in at least one valid diagram consistent with the given statements, not whether it must always be true — so the correct method is to try to draw a diagram where the proposed conclusion holds without contradicting any given statement.
Unlike “definitely true” conclusions, which must hold in every possible diagram consistent with the premises, a possibility is confirmed the moment a single valid, non-contradictory diagram can be drawn showing it. The standard technique is to take the most restrictive or “worst case” diagram first — the one that seems to rule the conclusion out — and check whether an alternative diagram, still consistent with all premises, can be constructed where the conclusion holds instead. Certain statement forms leave real ambiguity: "Some A are B" leaves open whether all A are B or only some, and that residual ambiguity is exactly where possibilities live. A possibility conclusion is only false if every conceivable diagram consistent with the premises rules it out entirely.
- Turns an abstract logic puzzle into a concrete diagram-drawing exercise
- Clarifies the difference between “definitely true” and “possibly true” conclusions
- Systematically checks the ambiguous residue left by “some” statements
AI Mentor Explanation
Given "All bowlers are athletes" and "Some athletes are left-handed," the claim “some bowlers are left-handed” is not guaranteed, but it is possible: draw a diagram where the left-handed athletes happen to overlap with the bowler circle, and nothing in the premises forbids that. Because “some athletes are left-handed” leaves the exact identity of those left-handed athletes ambiguous, a diagram where they coincide with bowlers is just as valid as one where they don’t. Possibility questions are confirmed the moment one such non-contradictory diagram exists, regardless of whether other valid diagrams show the opposite.
Worked example
Given
- All cats are pets
- Some pets are dogs
Test conclusion
- Some cats are dogs?
Verdict
- Possible — one valid diagram supports it
Step-by-Step Explanation
Step 1
List every given premise
Note whether each is universal (All/No) or particular (Some).
Step 2
Locate the ambiguous “some” statements
These are where multiple valid diagrams can differ.
Step 3
Attempt to draw a diagram supporting the conclusion
If one non-contradictory diagram exists, the possibility holds.
Step 4
Confirm no premise is violated
The diagram must still satisfy every given statement exactly.
What Interviewer Expects
- Clear distinction between “definitely true” and “possibly true” conclusions
- Correctly identifying which given statements leave ambiguity
- Constructing one valid diagram to confirm a possibility
- Not confusing possibility with certainty when checking multiple diagrams
Common Mistakes
- Treating a possibility question as if it required the conclusion to always hold
- Ignoring the ambiguity in “some” statements and assuming a fixed diagram
- Concluding “not possible” without actually attempting to construct a supporting diagram
- Confusing “some” with “only some”, over-restricting the diagram unnecessarily
Best Answer (HR Friendly)
“For possibility questions, I remind myself the bar is much lower than for definite conclusions — I just need to find one valid diagram, consistent with every given statement, where the conclusion holds. I look specifically at “some” statements because they’re the ones that leave room for different valid diagrams, and I try to draw the overlap in a way that supports the conclusion before ruling it out.”
Follow-up Questions
- How does a “possibility” verdict differ from a “definitely true” verdict in syllogisms?
- Can a conclusion be both “definitely false” and never possible under any diagram?
- How do multiple premises combine to narrow down which diagrams are valid?
- How would you explain why “some A are not B” leaves more ambiguity than “some A are B”?
MCQ Practice
1. Statements: All pens are tools. Some tools are red. Conclusion: Some pens are red. This conclusion is?
Since “some tools are red” does not specify which tools, a diagram can place red tools inside the pen subset without contradiction, making it possible but not certain.
2. A conclusion is confirmed as “possible” in a syllogism when?
Possibility only requires one non-contradictory diagram supporting the conclusion, unlike certainty which requires all diagrams to support it.
3. Statements: No fish are birds. All birds are winged. Conclusion: Some fish are winged. This is?
Fish and birds are fully disjoint, and all birds are winged, so no fish can be winged in any valid diagram — the conclusion is definitely false.
Flash Cards
What confirms a syllogism “possibility” conclusion? — One valid, non-contradictory diagram where the conclusion holds.
Where does ambiguity usually come from? — "Some" statements, which don’t specify exact overlap.
Possibility vs definitely true? — Possibility needs one supporting diagram; definitely true needs all diagrams to support it.
When is a possibility false? — Only when every valid diagram consistent with the premises rules it out.