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Syllogism questions with answers

Syllogism questions are decided by what must follow, never by what could. Each of the fifteen below is checked against every arrangement the statements permit, so a conclusion is marked to follow only when no counter-diagram exists. The walkthroughs name the counter-diagram when one does, which is the part a summary answer key leaves out.

Download the PDF — 15 questions with answers

Free, ungated, no email. This is the syllogism questions with answers PDF — the same 15 questions as below, with every worked solution at the back, ready to print.

How to use this set

The 15 questions below are ordered the way an exam block is rather than easiest-first: two gentle openers, then a run of medium, and a hard one every sixth question — 2 of the 15 sit in the hard band. Every question is a syllogism (statements & conclusions).

Work each question on paper before you open its solution. The walkthrough is the method itself, step for step, so reading it first turns a practice set into a reading exercise and teaches nothing. If you are stuck on the method rather than on one question, the method guide is a better place to start than the next question: Syllogism: the possibility rules that decide it.

15 syllogism questions with answers

Every question below was generated by the same engine that mints the Deduce daily puzzle round, and machine-checked before it reached this page — a multiple-choice question validates its own answer against its own options at generation, and ships only with a walkthrough attached. The walkthrough is the engine's own.

Question 1

Take the two statements to be true even if they differ from commonly known facts, then decide which conclusion logically follows.

Statements: All towns are regions. No regions are states.

Conclusion I: Some states are not towns.

Conclusion II: No states are towns.

  1. Only conclusion I follows
  2. Only conclusion II follows
  3. Either conclusion I or II follows
  4. Neither conclusion I nor II follows
  5. Both conclusions I and II follow
Show the worked solution
  1. Conclusion I ("Some states are not towns") need not follow — the statements allow a situation where it is false.
  2. Conclusion II ("No states are towns") is true in every situation the statements allow.
  3. So only conclusion II follows.

Question 2

Take the two statements to be true even if they differ from commonly known facts, then decide which conclusion logically follows.

Statements: All stools are chairs. All chairs are desks.

Conclusion I: All stools are desks.

Conclusion II: All desks are stools.

  1. Only conclusion I follows
  2. Only conclusion II follows
  3. Either conclusion I or II follows
  4. Neither conclusion I nor II follows
  5. Both conclusions I and II follow
Show the worked solution
  1. Conclusion I ("All stools are desks") is true in every situation the statements allow.
  2. Conclusion II ("All desks are stools") need not follow — the statements allow a situation where it is false.
  3. So only conclusion I follows.

Question 3

Take the two statements to be true even if they differ from commonly known facts, then decide which conclusion logically follows.

Statements: All cities are towns. No towns are states.

Conclusion I: No cities are states.

Conclusion II: No states are cities.

  1. Only conclusion I follows
  2. Only conclusion II follows
  3. Either conclusion I or II follows
  4. Neither conclusion I nor II follows
  5. Both conclusions I and II follow
Show the worked solution
  1. Conclusion I ("No cities are states") is true in every situation the statements allow.
  2. Conclusion II ("No states are cities") is true in every situation the statements allow.
  3. So both conclusions follow.

Question 4

Take the two statements to be true even if they differ from commonly known facts, then decide which conclusion logically follows.

Statements: No managers are doctors. No doctors are engineers.

Conclusion I: No engineers are managers.

Conclusion II: Some managers are not engineers.

  1. Only conclusion I follows
  2. Only conclusion II follows
  3. Either conclusion I or II follows
  4. Neither conclusion I nor II follows
  5. Both conclusions I and II follow
Show the worked solution
  1. Conclusion I ("No engineers are managers") need not follow — the statements allow a situation where it is false.
  2. Conclusion II ("Some managers are not engineers") need not follow — the statements allow a situation where it is false.
  3. So neither conclusion follows.

Question 5

Take the two statements to be true even if they differ from commonly known facts, then decide which conclusion logically follows.

Statements: Some vans are vehicles. No vehicles are buses.

Conclusion I: Some vans are not buses.

Conclusion II: All vans are buses.

  1. Only conclusion I follows
  2. Only conclusion II follows
  3. Either conclusion I or II follows
  4. Neither conclusion I nor II follows
  5. Both conclusions I and II follow
Show the worked solution
  1. Conclusion I ("Some vans are not buses") is true in every situation the statements allow.
  2. Conclusion II ("All vans are buses") need not follow — the statements allow a situation where it is false.
  3. So only conclusion I follows.

Question 6

Take the two statements to be true even if they differ from commonly known facts, then decide which conclusion logically follows.

Statements: All cars are buses. No buses are trains.

Conclusion I: No trains are cars.

Conclusion II: No cars are trains.

  1. Only conclusion I follows
  2. Only conclusion II follows
  3. Either conclusion I or II follows
  4. Neither conclusion I nor II follows
  5. Both conclusions I and II follow
Show the worked solution
  1. Conclusion I ("No trains are cars") is true in every situation the statements allow.
  2. Conclusion II ("No cars are trains") is true in every situation the statements allow.
  3. So both conclusions follow.

Question 7

Take the two statements to be true even if they differ from commonly known facts, then decide which conclusion logically follows.

Statements: All chairs are shelves. All shelves are cupboards.

Conclusion I: All chairs are cupboards.

Conclusion II: Some chairs are cupboards.

  1. Only conclusion I follows
  2. Only conclusion II follows
  3. Either conclusion I or II follows
  4. Neither conclusion I nor II follows
  5. Both conclusions I and II follow
Show the worked solution
  1. Conclusion I ("All chairs are cupboards") is true in every situation the statements allow.
  2. Conclusion II ("Some chairs are cupboards") need not follow — the statements allow a situation where it is false.
  3. So only conclusion I follows.

Question 8

Take the two statements to be true even if they differ from commonly known facts, then decide which conclusion logically follows.

Statements: No towns are regions. All regions are districts.

Conclusion I: Some towns are districts.

Conclusion II: No towns are districts.

  1. Only conclusion I follows
  2. Only conclusion II follows
  3. Either conclusion I or II follows
  4. Neither conclusion I nor II follows
  5. Both conclusions I and II follow
Show the worked solution
  1. Conclusion I ("Some towns are districts") need not follow — the statements allow a situation where it is false.
  2. Conclusion II ("No towns are districts") need not follow — the statements allow a situation where it is false.
  3. Conclusions I and II are a complementary pair — exactly one must be true in every case, but the statements do not fix which. So either I or II follows.

Question 9

Take the two statements to be true even if they differ from commonly known facts, then decide which conclusion logically follows.

Statements: Some rabbits are horses. All horses are cows.

Conclusion I: Some cows are rabbits.

Conclusion II: Some rabbits are cows.

  1. Only conclusion I follows
  2. Only conclusion II follows
  3. Either conclusion I or II follows
  4. Neither conclusion I nor II follows
  5. Both conclusions I and II follow
Show the worked solution
  1. Conclusion I ("Some cows are rabbits") is true in every situation the statements allow.
  2. Conclusion II ("Some rabbits are cows") is true in every situation the statements allow.
  3. So both conclusions follow.

Question 10

Take the two statements to be true even if they differ from commonly known facts, then decide which conclusion logically follows.

Statements: All pens are diaries. No diaries are notebooks.

Conclusion I: No pens are notebooks.

Conclusion II: All notebooks are pens.

  1. Only conclusion I follows
  2. Only conclusion II follows
  3. Either conclusion I or II follows
  4. Neither conclusion I nor II follows
  5. Both conclusions I and II follow
Show the worked solution
  1. Conclusion I ("No pens are notebooks") is true in every situation the statements allow.
  2. Conclusion II ("All notebooks are pens") need not follow — the statements allow a situation where it is false.
  3. So only conclusion I follows.

Question 11

Take the two statements to be true even if they differ from commonly known facts, then decide which conclusion logically follows.

Statements: All trains are scooters. No scooters are cars.

Conclusion I: No trains are cars.

Conclusion II: Some cars are not trains.

  1. Only conclusion I follows
  2. Only conclusion II follows
  3. Either conclusion I or II follows
  4. Neither conclusion I nor II follows
  5. Both conclusions I and II follow
Show the worked solution
  1. Conclusion I ("No trains are cars") is true in every situation the statements allow.
  2. Conclusion II ("Some cars are not trains") need not follow — the statements allow a situation where it is false.
  3. So only conclusion I follows.

Question 12

Take the two statements to be true even if they differ from commonly known facts, then decide which conclusion logically follows.

Statements: No books are papers. Some papers are notebooks.

Conclusion I: Some books are not notebooks.

Conclusion II: Some notebooks are not books.

  1. Only conclusion I follows
  2. Only conclusion II follows
  3. Either conclusion I or II follows
  4. Neither conclusion I nor II follows
  5. Both conclusions I and II follow
Show the worked solution
  1. Conclusion I ("Some books are not notebooks") need not follow — the statements allow a situation where it is false.
  2. Conclusion II ("Some notebooks are not books") is true in every situation the statements allow.
  3. So only conclusion II follows.

Question 13

Take the two statements to be true even if they differ from commonly known facts, then decide which conclusion logically follows.

Statements: All trays are cups. No cups are glasses.

Conclusion I: No glasses are trays.

Conclusion II: No trays are glasses.

  1. Only conclusion I follows
  2. Only conclusion II follows
  3. Either conclusion I or II follows
  4. Neither conclusion I nor II follows
  5. Both conclusions I and II follow
Show the worked solution
  1. Conclusion I ("No glasses are trays") is true in every situation the statements allow.
  2. Conclusion II ("No trays are glasses") is true in every situation the statements allow.
  3. So both conclusions follow.

Question 14

Take the two statements to be true even if they differ from commonly known facts, then decide which conclusion logically follows.

Statements: No stools are desks. No desks are benches.

Conclusion I: No stools are benches.

Conclusion II: Some benches are stools.

  1. Only conclusion I follows
  2. Only conclusion II follows
  3. Either conclusion I or II follows
  4. Neither conclusion I nor II follows
  5. Both conclusions I and II follow
Show the worked solution
  1. Conclusion I ("No stools are benches") need not follow — the statements allow a situation where it is false.
  2. Conclusion II ("Some benches are stools") need not follow — the statements allow a situation where it is false.
  3. Conclusions I and II are a complementary pair — exactly one must be true in every case, but the statements do not fix which. So either I or II follows.

Question 15

Take the two statements to be true even if they differ from commonly known facts, then decide which conclusion logically follows.

Statements: Some managers are officers. No officers are teachers.

Conclusion I: No teachers are managers.

Conclusion II: Some managers are not teachers.

  1. Only conclusion I follows
  2. Only conclusion II follows
  3. Either conclusion I or II follows
  4. Neither conclusion I nor II follows
  5. Both conclusions I and II follow
Show the worked solution
  1. Conclusion I ("No teachers are managers") need not follow — the statements allow a situation where it is false.
  2. Conclusion II ("Some managers are not teachers") is true in every situation the statements allow.
  3. So only conclusion II follows.
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Where these questions come from

Most free practice for this topic is a scanned upload or a blog quiz, and neither can tell you a question has exactly one answer. That is the one thing this set can promise: it is minted, not typed. The engine behind it serves Deduce's daily puzzle round, so the questions here are the same shape as the ones a live round would give you — and there is an unlimited supply of them, which is why this page can be regenerated rather than padded.

If you want the method rather than more questions, Syllogism: the possibility rules that decide it covers the approach, the traps and a worked table. This page and that one deliberately answer different questions: that one is how do I solve these, this one is give me syllogism questions with the answers.

FAQ

What does 'possibility' mean in a syllogism question?

A possibility conclusion follows if at least one valid diagram supports it. A definite conclusion follows only if every valid diagram supports it. Mixing the two is the single most common error: candidates apply the 'every diagram' test to a possibility statement and reject a correct answer.

Can two negative statements ever give a definite conclusion?

No. From 'No A is B' and 'No B is C' nothing definite follows about A and C, because they may overlap entirely, partly, or not at all. Any option claiming a definite relation there is a distractor, and it appears often enough to be worth recognising on sight.

Is the Venn method faster than the rules?

For two-statement questions the rules are faster once memorised. For three statements, or anything with 'only a few', draw. A drawing that admits two shapes is a proof of non-conclusion, and it takes about fifteen seconds — far less than re-reading the statements for the third time.

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