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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 DeducePuzzles 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: No dogs are tigers. All tigers are rabbits.

Conclusion I: All dogs are rabbits.

Conclusion II: Some rabbits are not dogs.

  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 dogs are rabbits") need not follow — the statements allow a situation where it is false.
  2. Conclusion II ("Some rabbits are not dogs") 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: No oranges are fruits. All fruits are guavas.

Conclusion I: Some guavas are not oranges.

Conclusion II: No oranges are guavas.

  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 guavas are not oranges") is true in every situation the statements allow.
  2. Conclusion II ("No oranges are guavas") 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: No lilies are roses. Some roses are orchids.

Conclusion I: All orchids are lilies.

Conclusion II: No lilies are orchids.

  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 orchids are lilies") need not follow — the statements allow a situation where it is false.
  2. Conclusion II ("No lilies are orchids") need not follow — the statements allow a situation where it is false.
  3. So neither conclusion follows.

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 singers are painters. Some painters are players.

Conclusion I: Some players are singers.

Conclusion II: No players are singers.

  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 players are singers") need not follow — the statements allow a situation where it is false.
  2. Conclusion II ("No players are singers") 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 5

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

Statements: Some mangoes are apples. No apples are grapes.

Conclusion I: All mangoes being grapes is a possibility.

Conclusion II: Some grapes being mangoes is a possibility.

  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 mangoes being grapes is a possibility") does not follow — no situation the statements allow makes it true.
  2. Conclusion II ("Some grapes being mangoes is a possibility") follows — the statements allow a situation in which it is true.
  3. So only conclusion II follows.

Question 6

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

Statements: No lawyers are teachers. Only a few teachers are managers. Some managers are officers.

Conclusion I: Some managers are teachers.

Conclusion II: Some lawyers being officers is a possibility.

  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 managers are teachers") is true in every situation the statements allow.
  2. Conclusion II ("Some lawyers being officers is a possibility") follows — the statements allow a situation in which it is true.
  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 lawyers are managers. No managers are doctors.

Conclusion I: Some doctors are lawyers.

Conclusion II: All doctors are lawyers.

  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 doctors are lawyers") need not follow — the statements allow a situation where it is false.
  2. Conclusion II ("All doctors are lawyers") need not follow — the statements allow a situation where it is false.
  3. So neither conclusion 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 files are papers. All papers are pencils.

Conclusion I: No pencils are files.

Conclusion II: Some pencils are files.

  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 pencils are files") need not follow — the statements allow a situation where it is false.
  2. Conclusion II ("Some pencils are files") 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: All lawyers are doctors. All doctors are clerks.

Conclusion I: No lawyers are clerks.

Conclusion II: Some lawyers are clerks.

  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 lawyers are clerks") need not follow — the statements allow a situation where it is false.
  2. Conclusion II ("Some lawyers are clerks") is true in every situation the statements allow.
  3. So only conclusion II follows.

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 bottles are trays. No trays are plates.

Conclusion I: Some bottles are not plates.

Conclusion II: Some plates are not bottles.

  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 bottles are not plates") is true in every situation the statements allow.
  2. Conclusion II ("Some plates are not bottles") is true in every situation the statements allow.
  3. So both conclusions follow.

Question 11

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

Statements: Some actors are writers. Some writers are dancers.

Conclusion I: Some dancers are not actors.

Conclusion II: Some dancers are actors.

  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 dancers are not actors") need not follow — the statements allow a situation where it is false.
  2. Conclusion II ("Some dancers are actors") need not follow — the statements allow a situation where it is false.
  3. So neither conclusion follows.

Question 12

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

Statements: Some bananas are not fruits. Some fruits are not apples. All apples are oranges.

Conclusion I: All bananas being apples is a possibility.

Conclusion II: Some fruits being apples is a possibility.

  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 bananas being apples is a possibility") follows — the statements allow a situation in which it is true.
  2. Conclusion II ("Some fruits being apples is a possibility") follows — the statements allow a situation in which it is true.
  3. So both conclusions follow.

Question 13

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

Statements: No cows are rabbits. All rabbits are horses.

Conclusion I: No cows are horses.

Conclusion II: Some cows are horses.

  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 cows are horses") need not follow — the statements allow a situation where it is false.
  2. Conclusion II ("Some cows are horses") 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 14

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

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

Conclusion I: Some pens are notebooks.

Conclusion II: Some notebooks are not 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 ("Some pens are notebooks") need not follow — the statements allow a situation where it is false.
  2. Conclusion II ("Some notebooks are not pens") is true in every situation the statements allow.
  3. So only conclusion 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: All rabbits are cats. Some cats are pets.

Conclusion I: Some rabbits being pets is a possibility.

Conclusion II: Some pets being rabbits is a possibility.

  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 rabbits being pets is a possibility") follows — the statements allow a situation in which it is true.
  2. Conclusion II ("Some pets being rabbits is a possibility") follows — the statements allow a situation in which it is true.
  3. So both conclusions follow.
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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 DeducePuzzles'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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