Syllogism Quiz: Reasoning Practice with Possibility

Spoilers! These are the Starter quiz’s answers. Easy, Medium, Hard and Mixed rounds show their own answers when you finish.

1. Statements: All pens are books. Some books are bags. Conclusions: I. Some pens are bags. II. Some bags are books.

   • Only I follows
   • Only II follows
   • Neither I nor II follows
   • Both I and II follow

   Answer: Only II follows. 'Some books are bags' converts directly to 'Some bags are books', so II follows. The books that are bags need not include any pen, so I is not certain.

2. Statements: No cup is a plate. All plates are bowls. Conclusions: I. Some bowls are not cups. II. Some cups are bowls.

   • Only I follows
   • Only II follows
   • Neither I nor II follows
   • Both I and II follow

   Answer: Only I follows. The plates are bowls and none of them is a cup, so at least those bowls are not cups — I follows. Cups may or may not overlap the rest of the bowls, so II is not definite.

3. Statements: Some keys are locks. All locks are doors. No door is a window. Conclusions: I. Some keys are doors. II. Some keys are not windows.

   • Only I follows
   • Only II follows
   • Either I or II follows
   • Both I and II follow

   Answer: Both I and II follow. The keys that are locks are also doors, so I follows. Those same keys, being doors, cannot be windows, so II follows too.

4. Statements: All roses are flowers. Some flowers are plants. Conclusions: I. All roses being plants is a possibility. II. Some plants are roses.

   • Only I follows
   • Only II follows
   • Neither I nor II follows
   • Both I and II follow

   Answer: Only I follows. The plant circle may be drawn to cover all the roses without breaking any statement, so the possibility in I holds. It is only a possibility, so the definite claim in II does not follow.

5. Statements: No tiger is a lion. Some lions are cats. Conclusions: I. Some cats are not tigers. II. All tigers being cats is a possibility.

   • Only I follows
   • Only II follows
   • Neither I nor II follows
   • Both I and II follow

   Answer: Both I and II follow. The cats that are lions can never be tigers, so I is definite. Tigers can still sit inside the part of 'cats' that is not lions, so II is possible.

6. Statements: Some apples are mangoes. Some mangoes are grapes. Conclusions: I. Some apples are grapes. II. No apple is a grape.

   • Only I follows
   • Only II follows
   • Either I or II follows
   • Neither I nor II follows

   Answer: Either I or II follows. Two 'some' statements give no definite link between apples and grapes, so neither is certain alone. But I and II are about the same two terms and one of them must be true — either I or II follows.

7. Statements: All doctors are teachers. No teacher is a singer. Conclusions: I. Some singers being doctors is a possibility. II. No singer is a doctor.

   • Only I follows
   • Only II follows
   • Either I or II follows
   • Both I and II follow

   Answer: Only II follows. Every doctor is a teacher and no teacher is a singer, so no doctor can be a singer. II is definite and the possibility in I is ruled out.

8. Statements: All cars are buses. Some buses are trains. No train is a ship. Conclusions: I. No car is a ship. II. Some cars are trains.

   • Only I follows
   • Only II follows
   • Neither I nor II follows
   • Both I and II follow

   Answer: Neither I nor II follows. The buses that are trains need not include any car, so II fails. Only trains are barred from being ships; cars may still overlap ships, so I fails too.

9. Statements: Only a few pencils are erasers. No eraser is a sharpener. Conclusions: I. Some pencils are not erasers. II. All sharpeners are pencils.

   • Only I follows
   • Only II follows
   • Either I or II follows
   • Neither I nor II follows

   Answer: Only I follows. 'Only a few A are B' means some A are B and some A are not B, so I follows directly. Nothing ties sharpeners to pencils definitely, so II does not follow.

10. Statements: Some boxes are cartons. All cartons are bags. Conclusions: I. All boxes are bags. II. No box is a bag.

    • Only I follows
    • Only II follows
    • Either I or II follows
    • Neither I nor II follows

    Answer: Neither I nor II follows. The boxes that are cartons are bags, so 'Some boxes are bags' is definite and II is false. I is not certain. As II is definitely false, this is not an either-or pair: neither follows.