How to Solve Syllogism Problems
Solve syllogism aptitude problems using the Venn diagram method — validate conclusions correctly with worked examples and practice questions.
Expected Interview Answer
Syllogism problems are solved by drawing Venn diagrams for each given statement and then checking which conclusions are true in every possible diagram consistent with those statements, not just the most obvious one.
Each statement — "All A are B", "Some A are B", "No A are B", "Some A are not B" — restricts how two circles can overlap. Draw every diagram permitted by the premises, including the least-obvious valid arrangements, because a conclusion is only "definitely true" if it holds in all of them. Combine the diagrams for both statements before evaluating the conclusion. A common trap is assuming a conclusion is true because it feels intuitive when in fact an alternative valid diagram breaks it.
- Venn diagrams make abstract statements visual and checkable
- Testing all valid diagrams avoids false-positive conclusions
- One method scales to two-, three- and complex multi-statement syllogisms
AI Mentor Explanation
Consider "All spinners are bowlers" and "Some bowlers are all-rounders". You cannot conclude "some spinners are all-rounders", because the all-rounders overlapping with bowlers might be entirely outside the spinner group — draw the circles and you will find a valid arrangement where spinners and all-rounders never touch. Syllogism problems demand exactly this discipline: draw every diagram the statements permit, and only accept a conclusion that holds in all of them, not the one that merely feels plausible.
Step-by-Step Explanation
Step 1
Draw a diagram per statement
Represent "All A are B", "Some A are B", "No A are B" as circle relationships.
Step 2
Enumerate all valid combinations
Where a statement allows multiple diagrams, draw each one, not just the obvious case.
Step 3
Overlay both statements
Combine the diagrams for statement 1 and statement 2 consistently.
Step 4
Test the conclusion against every diagram
A conclusion is valid only if it holds true in every combined diagram, not just some.
What Interviewer Expects
- Correct Venn-diagram translation of All/Some/No statements
- Enumerating every diagram a statement permits, not just one
- Testing conclusions across all valid diagrams before accepting them
- Recognising "possibility" vs "definite" conclusions
Common Mistakes
- Accepting an intuitive-but-unproven conclusion
- Drawing only one diagram when a statement allows several
- Confusing "Some A are B" with "Some A are not B"
- Ignoring the reverse direction (Some A are B implies Some B are A)
Best Answer (HR Friendly)
“I convert each statement into a Venn diagram, and where a statement allows more than one valid arrangement, I draw all of them. Then I only accept a conclusion as definitely true if it holds across every single diagram, not just the one that looks obvious at first glance — that discipline is what actually separates correct from incorrect syllogism answers.”
Follow-up Questions
- How do you handle syllogisms with three statements instead of two?
- What is the difference between a "definite" and a "possible" conclusion?
- How does "Some A are not B" restrict the Venn diagram differently from "No A are B"?
- How would you solve a syllogism with either/or conclusions?
MCQ Practice
1. Statements: All cats are animals. All animals are living things. Conclusion: All cats are living things. Is this valid?
This is a straightforward transitive chain of "All" statements — the cat circle sits fully inside animals, which sits fully inside living things, so the conclusion is definitely valid.
2. Statements: All doctors are professionals. Some professionals are wealthy. Conclusion: Some doctors are wealthy. Is this valid?
A valid diagram exists where the wealthy professionals are entirely outside the doctor circle, so the conclusion does not follow definitely — it is invalid.
3. What is the correct diagram interpretation of "No A are B"?
"No A are B" means the two circles are completely separate, with no shared region at all.
Flash Cards
How do you diagram "All A are B"? — Circle A drawn entirely inside circle B.
How do you diagram "No A are B"? — Circles A and B with zero overlap, completely separate.
When is a conclusion valid? — Only when it holds true in every diagram permitted by the given statements.
Common trap in syllogisms? — Accepting an intuitive conclusion without checking all alternative valid diagrams.