Syllogism questions with solutions

1. Question 1Easy

   Statements: All apples are fruits. All fruits are sweet. Conclusions: I. All apples are sweet. II. Some sweet things are apples. Which conclusion(s) follow?

   • A.Only I follows
   • B.Only II follows
   • C.Both I and II followCorrect
   • D.Neither I nor II follows
   • E.Either I or II follows
   Show solution

   Apples ⊆ fruits ⊆ sweet, so both conclusions hold.

2. Question 2Easy

   Statements: Some cars are buses. All buses are trucks. Conclusions: I. Some cars are trucks. II. Some trucks are cars.

   • A.Only conclusion I follows
   • B.Only conclusion II follows
   • C.Both conclusions followCorrect
   • D.Neither conclusion follows
   • E.Either conclusion I or II follows
   Show solution

   Some cars are buses and all buses are trucks, so those cars are trucks, giving conclusion I. Since some cars are trucks, some trucks are cars is the valid converse, giving conclusion II. Both follow.

3. Question 3Easy

   Statements: All pens are books. All books are papers. Conclusions: I. All pens are papers. II. Some papers are pens.

   • A.Only conclusion I follows
   • B.Only conclusion II follows
   • C.Both conclusions followCorrect
   • D.Neither conclusion follows
   • E.Either conclusion I or II follows
   Show solution

   All pens are books and all books are papers chain together, so all pens are papers, which validates conclusion I. Since all pens are papers, at least some papers are pens, which is the valid converse and validates conclusion II. Both follow.

4. Question 4Easy

   Statements: All cats are animals. All animals are living things. Conclusion: All cats are living things.

   • A.The conclusion followsCorrect
   • B.Data are inadequate
   • C.The conclusion only partly follows
   • D.The conclusion does not follow
   Show solution

   If every cat is an animal and every animal is a living thing, then every cat must be a living thing, so the conclusion follows.

5. Question 5Easy

   Statements: Some doctors are engineers. All engineers are rich. Conclusion: Some doctors are rich.

   • A.The conclusion followsCorrect
   • B.The conclusion does not follow
   • C.Data are inadequate
   • D.Cannot be determined
   Show solution

   The doctors who are engineers are rich, since all engineers are rich, so some doctors are rich. The conclusion follows.

6. Question 6Moderate

   Statements: Some pens are pencils. All pencils are erasers. Conclusions: I. Some pens are erasers. II. All erasers are pens. Which conclusion(s) follow?

   • A.Only I followsCorrect
   • B.Only II follows
   • C.Both I and II follow
   • D.Neither I nor II follows
   • E.Either I or II follows
   Show solution

   The pens that are pencils must be erasers, so I follows; nothing forces all erasers to be pens.

7. Question 7Moderate

   Statements: All metals are conductors. Some conductors are liquids. Conclusions: I. Some metals are liquids. II. Some liquids are conductors. Which follows?

   • A.Only II followsCorrect
   • B.Only I follows
   • C.Both I and II follow
   • D.Neither follows
   Show solution

   Conclusion I is not necessarily true — metals being conductors does not guarantee any metal is a liquid. Conclusion II follows because some conductors are liquids, so some liquids are certainly conductors.

8. Question 8Moderate

   Statements: All books are pens. All pens are chairs. Conclusions: I. All books are chairs. II. Some chairs are books. Which conclusion follows?

   • A.Only I
   • B.Only II
   • C.Both I and IICorrect
   • D.Neither I nor II
   Show solution

   Books are pens and pens are chairs, so all books are chairs (I). Since books are also chairs and books exist, some chairs are books (II). Both follow.

9. Question 9Moderate

   Statements: No pen is a pencil. All pencils are erasers. Conclusions: I. Some erasers are not pens. II. No pen is an eraser.

   • A.Only conclusion I followsCorrect
   • B.Only conclusion II follows
   • C.Both conclusions follow
   • D.Neither conclusion follows
   • E.Either conclusion I or II follows
   Show solution

   All pencils are erasers and no pen is a pencil, so pencils are erasers that are not pens, which guarantees some erasers are not pens: conclusion I follows. Conclusion II is too strong, since some erasers could still be pens, so it does not follow.

10. Question 10Moderate

    Statements: Some cats are dogs. No dog is white. Conclusions: I. Some cats are not white. II. All cats are white.

    • A.Only conclusion I followsCorrect
    • B.Only conclusion II follows
    • C.Both conclusions follow
    • D.Neither conclusion follows
    • E.Either conclusion I or II follows
    Show solution

    Some cats are dogs, and no dog is white, so those cats that are dogs cannot be white. That guarantees some cats are not white, validating conclusion I. Conclusion II claims all cats are white, which the same reasoning rules out. Only I follows.

11. Question 11Moderate

    Statements: All roses are flowers. Some flowers are red. Conclusions: I. Some roses are red. II. Some flowers are roses.

    • A.Only conclusion I follows
    • B.Only conclusion II followsCorrect
    • C.Both conclusions follow
    • D.Neither conclusion follows
    • E.Either conclusion I or II follows
    Show solution

    All roses are flowers, so some flowers are roses is a valid converse, validating conclusion II. The red flowers need not include any rose, so some roses are red is only a possibility, not a certainty, and conclusion I does not follow. Only II follows.

12. Question 12Moderate

    Statements: All pens are books. All books are red. Conclusions: I. All pens are red. II. Some red things are pens. Which conclusion follows?

    • A.Both I and II followCorrect
    • B.Only I follows
    • C.Only II follows
    • D.Neither follows
    Show solution

    All pens are books and all books are red, so all pens are red — I follows. If all pens are red, then some red things are certainly pens — II follows. Both follow.

These are 12 of 33 syllogism questions in the bank. Attempt the rest with instant feedback in the practice drills, or under a clock in the mock tests.