Syllogism Questions with Answers
Syllogism questions give two or three statements and ask which conclusions must follow. Treat the statements as true even if they clash with real life, draw Venn diagrams, and accept a conclusion only if it holds in every possible diagram. Four statement types and a short list of rules cover almost every question you will see.
Syllogisms are one of the most commonly reported reasoning topics in placement tests. Our guides to Infosys, Accenture and Cognizant all list them, and they go well with blood relations and coding-decoding.
What Is a Syllogism Question?
You are given statements such as “All pens are books” and “Some books are bags”, followed by conclusions such as “Some pens are bags”. Your job is to decide which conclusions are certain. The statements are your only facts. If a statement says “All cats are dogs”, accept it, even though it’s false in the real world.
The Four Statement Types
| Statement | Meaning | Venn picture |
|---|---|---|
| All A are B | Every A is a B | A sits completely inside B |
| No A is B | Nothing is both A and B | Two separate circles |
| Some A are B | At least one A is a B | The circles overlap |
| Some A are not B | At least one A is outside B | Part of A lies outside B |
Conversions you can rely on:
- “All A are B” gives “Some B are A”.
- “No A is B” gives “No B is A”.
- “Some A are B” gives “Some B are A”.
- “Some A are not B” has no valid conversion. “Some B are not A” does not follow.
A note on convention: aptitude tests treat a universal statement as also implying its “some” version, so “All A are B” implies “Some A are B”, and “No A is B” implies “Some A are not B”. Formal logic textbooks are stricter, but the tests follow this convention, so use it.
Rules for Valid Conclusions
Two statements that share a middle term (B) give a definite conclusion only in these patterns:
| Statements | Conclusion |
|---|---|
| All A are B + All B are C | All A are C |
| All A are B + No B is C | No A is C |
| Some A are B + All B are C | Some A are C |
| Some A are B + No B is C | Some A are not C |
| No A is B + All B are C | Some C are not A |
These patterns give no definite conclusion:
| Statements | Why |
|---|---|
| Some A are B + Some B are C | A and C may or may not overlap |
| All A are B + Some B are C | The part of B that is C may not touch A |
| No A is B + No B is C | A and C may overlap |
| All A are B + All C are B | A and C both sit inside B but may not meet |
The Venn Diagram Method
- Draw the statements as circles, starting with the most restrictive (“All” and “No”).
- Add the “Some” statements in every position they could occupy, since a “Some” statement can often be drawn in more than one way.
- Test each conclusion against every diagram. It follows only if it is true in all of them.
- For a “possibility” conclusion, it’s enough that it is true in at least one diagram.
Either-Or Cases
Sometimes neither conclusion follows on its own, but one of them has to be true. The question usually offers “Either I or II follows”. That’s correct when the two conclusions are a complementary pair about the same two terms, such as “Some A are B” and “No A is B”, or “All A are B” and “Some A are not B”. Together they cover every possibility, so one of them is true in each diagram.
Solved Examples
1. Statements: All cats are dogs. All dogs are birds. Conclusions: I. All cats are birds. II. Some birds are cats. Answer: both follow. The two statements chain to “All cats are birds” (I), and “All cats are birds” converts to “Some birds are cats” (II).
2. Statements: Some pens are books. All books are tables. Conclusions: I. Some pens are tables. II. All tables are books. Answer: only I follows. “Some A are B + All B are C” gives “Some A are C”. Conclusion II reverses “All books are tables”, which is not valid.
3. Statements: All flowers are trees. No tree is a stone. Conclusions: I. No flower is a stone. II. Some stones are not flowers. Answer: both follow. “All A are B + No B is C” gives “No A is C” (I). That converts to “No stone is a flower”, which implies “Some stones are not flowers” (II).
4. Statements: Some doctors are teachers. Some teachers are writers. Conclusions: I. Some doctors are writers. II. Some writers are doctors. Answer: neither follows. Two “Some” statements never give a definite conclusion, because the doctors who are teachers need not be the teachers who are writers.
5. Statements: All students are boys. Some boys are athletes. Conclusions: I. Some students are athletes. II. No student is an athlete. Answer: either I or II follows. Neither is certain, but they are a complementary pair about students and athletes, and in every diagram one of them is true.
6. Statements: Some bags are boxes. All boxes are cars. No car is a van. Conclusions: I. Some bags are cars. II. No box is a van. III. Some bags are not vans. Answer: all three follow. “Some bags are boxes + All boxes are cars” gives “Some bags are cars” (I). “All boxes are cars + No car is a van” gives “No box is a van” (II). “Some bags are cars + No car is a van” gives “Some bags are not vans” (III).
Common Mistakes
- Using real-world facts. If the statements say “All lions are birds”, treat it as true.
- Converting “Some A are not B”. It has no valid conversion.
- Treating a possibility as a certainty. “Some A are C” being possible does not mean it follows.
- Drawing only one diagram. A “Some” statement can often be placed in more than one way, so test your conclusion against each.
- Missing the either-or case. When two conclusions are a complementary pair and neither follows alone, check whether “either I or II” applies.
Practice Questions
Try each on paper, then check the answer.
1. Statements: All pens are pencils. Some pencils are erasers. Conclusions: I. Some pens are erasers. II. Some erasers are pencils. Answer: only II. “Some pencils are erasers” converts to “Some erasers are pencils”. Nothing certain links pens and erasers.
2. Statements: No tiger is a lion. All lions are animals. Conclusions: I. Some animals are not tigers. II. No lion is a tiger. Answer: both follow. “No A is B + All B are C” gives “Some C are not A” (I), and “No tiger is a lion” converts to “No lion is a tiger” (II).
3. Statements: All roses are flowers. Some flowers are red. Conclusions: I. Some roses are red. II. Some red things are flowers. Answer: only II. “Some flowers are red” converts to “Some red things are flowers”. The red flowers may include no roses.
4. Statements: Some cars are buses. All buses are trucks. Conclusions: I. Some cars are trucks. II. Some trucks are cars. Answer: both follow. “Some A are B + All B are C” gives “Some cars are trucks” (I), which converts to II.
5. Statements: No book is a pen. No pen is a bag. Conclusions: I. No book is a bag. II. Some books are bags. Answer: either I or II follows. Two “No” statements give nothing definite, but the conclusions are a complementary pair about books and bags.
6. Statements: All laptops are machines. All machines are tools. Conclusions: I. All laptops are tools. II. All tools are laptops. Answer: only I. The chain gives “All laptops are tools”. Conclusion II reverses it.
7. Statements: Some mangoes are fruits. No fruit is a stone. Conclusions: I. Some mangoes are not stones. II. No mango is a stone. Answer: only I. “Some A are B + No B is C” gives “Some A are not C”. Only some mangoes are known to be fruits, so “No mango is a stone” is not certain.
8. Statements: Some lamps are tables. Some tables are chairs. Conclusions: I. Some lamps are chairs. II. No lamp is a chair. Answer: either I or II follows. Two “Some” statements give nothing certain, but “Some lamps are chairs” and “No lamp is a chair” are a complementary pair.
Compare practice question 8 with solved example 4. In example 4 the two conclusions were not complementary, so neither follows. Here they are, so “either-or” applies.
Frequently Asked Questions
What is a syllogism in reasoning?
A syllogism is a set of two or three statements followed by conclusions. You decide which conclusions must be true, treating the statements as facts regardless of real-world truth.
How do I solve syllogism questions quickly?
Learn the rules table for the common patterns, and use Venn diagrams for anything unfamiliar. Draw the “All” and “No” statements first, then test each conclusion against every possible diagram.
What are the four types of syllogism statements?
“All A are B”, “No A is B”, “Some A are B” and “Some A are not B”. Each has its own Venn picture and its own valid conversion rules.
What does “either I or II follows” mean?
It applies when neither conclusion follows on its own, but together they form a complementary pair about the same two terms, so exactly one of them is true in any diagram.
Should I use real-world knowledge in syllogisms?
No. Treat the statements as true even if they sound absurd, and judge the conclusions only from them.
Which exams ask syllogism questions?
They appear in the reasoning sections of placement tests and in many bank and SSC exams. Our Infosys, Accenture and Cognizant guides list them among the commonly reported topics.