OU All In One

Syllogisms questions

Which conclusions follow from the statements.

1. Statements: 1. All phones are laptops. 2. All laptops are tablets. Conclusions: I. All phones are tablets. II. Some tablets are phones.

  1. Neither I nor II follows
  2. Only I follows
  3. Both I and II follow
  4. Only II follows
Answer

C. Both I and II follow All phones sit inside laptops, which sits inside tablets, so both are true.

2. Statements: 1. No phones is laptops. 2. No laptops is tablets. Conclusions: I. No phones is tablets. II. Some phones are tablets.

  1. Only I follows
  2. Either I or II follows
  3. Both I and II follow
  4. Only II follows
Answer

B. Either I or II follows Nothing links phones and tablets, but the two conclusions are opposites, so exactly one holds.

3. Statements: 1. All cars are buses. 2. Some trucks are not buses. Conclusions: I. Some trucks are not cars. II. All trucks are cars.

  1. Only II follows
  2. Neither I nor II follows
  3. Both I and II follow
  4. Only I follows
Answer

D. Only I follows The trucks outside buses are also outside cars (since all cars are inside buses).

4. Statements: 1. All apples are fruits. 2. Some fruits are seeds. Conclusions: I. Some apples are seeds. II. Some seeds are fruits.

  1. Both I and II follow
  2. Only I follows
  3. Neither I nor II follows
  4. Only II follows
Answer

D. Only II follows The seeds that are fruits need not be apples, so I does not follow; II is the converse of the second statement.

5. Statements: 1. All pens are books. 2. All pens are bags. Conclusions: I. Some books are bags. II. All books are bags.

  1. Neither I nor II follows
  2. Only II follows
  3. Only I follows
  4. Both I and II follow
Answer

C. Only I follows Every pens is both books and bags, so some books are bags. Not all books need be bags.

6. Statements: 1. Some doctors are teachers. 2. Some teachers are singers. Conclusions: I. Some doctors are singers. II. No doctors is singers.

  1. Only II follows
  2. Either I or II follows
  3. Only I follows
  4. Both I and II follow
Answer

B. Either I or II follows Neither is certain alone, but they are opposites covering every case, so one of them must be true.

7. Statements: 1. Some chairs are tables. 2. All tables are desks. Conclusions: I. Some chairs are desks. II. All desks are chairs.

  1. Both I and II follow
  2. Only I follows
  3. Only II follows
  4. Neither I nor II follows
Answer

B. Only I follows The chairs that are tables are also desks, so I follows. Nothing says all desks are chairs.

8. Statements: 1. Some phones are laptops. 2. Some laptops are tablets. Conclusions: I. Some phones are tablets. II. No phones is tablets.

  1. Only II follows
  2. Either I or II follows
  3. Both I and II follow
  4. Only I follows
Answer

B. Either I or II follows Neither is certain alone, but they are opposites covering every case, so one of them must be true.

9. Statements: 1. All cats are dogs. 2. All cats are birds. Conclusions: I. Some dogs are birds. II. All dogs are birds.

  1. Only II follows
  2. Only I follows
  3. Neither I nor II follows
  4. Both I and II follow
Answer

B. Only I follows Every cats is both dogs and birds, so some dogs are birds. Not all dogs need be birds.

10. Statements: 1. Some apples are fruits. 2. Some fruits are seeds. Conclusions: I. Some apples are seeds. II. No apples is seeds.

  1. Either I or II follows
  2. Only I follows
  3. Only II follows
  4. Both I and II follow
Answer

A. Either I or II follows Neither is certain alone, but they are opposites covering every case, so one of them must be true.

11. Statements: 1. No doctors is teachers. 2. No teachers is singers. Conclusions: I. No doctors is singers. II. Some doctors are singers.

  1. Only II follows
  2. Only I follows
  3. Both I and II follow
  4. Either I or II follows
Answer

D. Either I or II follows Nothing links doctors and singers, but the two conclusions are opposites, so exactly one holds.

12. Statements: 1. Some pens are books. 2. All books are bags. Conclusions: I. Some pens are bags. II. All bags are pens.

  1. Only II follows
  2. Both I and II follow
  3. Neither I nor II follows
  4. Only I follows
Answer

D. Only I follows The pens that are books are also bags, so I follows. Nothing says all bags are pens.

13. Statements: 1. All cars are buses. 2. No buses is trucks. Conclusions: I. No cars is trucks. II. Some trucks are cars.

  1. Only I follows
  2. Only II follows
  3. Both I and II follow
  4. Neither I nor II follows
Answer

A. Only I follows Every cars is a buses and no buses is a trucks, so no cars is a trucks; II contradicts I.

14. Statements: 1. All doctors are teachers. 2. All teachers are singers. Conclusions: I. All doctors are singers. II. Some singers are doctors.

  1. Both I and II follow
  2. Only I follows
  3. Neither I nor II follows
  4. Only II follows
Answer

A. Both I and II follow All doctors sit inside teachers, which sits inside singers, so both are true.

15. Statements: 1. No roses is flowers. 2. No flowers is plants. Conclusions: I. No roses is plants. II. Some roses are plants.

  1. Either I or II follows
  2. Both I and II follow
  3. Only I follows
  4. Only II follows
Answer

A. Either I or II follows Nothing links roses and plants, but the two conclusions are opposites, so exactly one holds.

16. Statements: 1. Some cats are dogs. 2. All dogs are birds. Conclusions: I. Some cats are birds. II. All birds are cats.

  1. Only II follows
  2. Only I follows
  3. Both I and II follow
  4. Neither I nor II follows
Answer

B. Only I follows The cats that are dogs are also birds, so I follows. Nothing says all birds are cats.

17. Statements: 1. Some cats are dogs. 2. No dogs is birds. Conclusions: I. Some cats are not birds. II. All cats are birds.

  1. Neither I nor II follows
  2. Only II follows
  3. Only I follows
  4. Both I and II follow
Answer

C. Only I follows The cats that are dogs cannot be birds, so some cats are not birds.

18. Statements: 1. No cars is buses. 2. All buses are trucks. Conclusions: I. Some trucks are not cars. II. No cars is trucks.

  1. Only II follows
  2. Only I follows
  3. Neither I nor II follows
  4. Both I and II follow
Answer

B. Only I follows Every buses is a trucks and no buses is an cars, so those trucks are not cars. cars and trucks may still overlap, so II does not follow.

19. Statements: 1. All pens are books. 2. Some bags are not books. Conclusions: I. Some bags are not pens. II. All bags are pens.

  1. Only I follows
  2. Both I and II follow
  3. Neither I nor II follows
  4. Only II follows
Answer

A. Only I follows The bags outside books are also outside pens (since all pens are inside books).

20. Statements: 1. Some cars are buses. 2. Some buses are trucks. Conclusions: I. Some cars are trucks. II. No cars is trucks.

  1. Both I and II follow
  2. Only I follows
  3. Either I or II follows
  4. Only II follows
Answer

C. Either I or II follows Neither is certain alone, but they are opposites covering every case, so one of them must be true.

21. Statements: 1. No apples is fruits. 2. No fruits is seeds. Conclusions: I. No apples is seeds. II. Some apples are seeds.

  1. Only I follows
  2. Both I and II follow
  3. Only II follows
  4. Either I or II follows
Answer

D. Either I or II follows Nothing links apples and seeds, but the two conclusions are opposites, so exactly one holds.

22. Statements: 1. All apples are fruits. 2. Some seeds are not fruits. Conclusions: I. Some seeds are not apples. II. All seeds are apples.

  1. Both I and II follow
  2. Only II follows
  3. Only I follows
  4. Neither I nor II follows
Answer

C. Only I follows The seeds outside fruits are also outside apples (since all apples are inside fruits).

23. Statements: 1. Some roses are flowers. 2. No flowers is plants. Conclusions: I. Some roses are not plants. II. All roses are plants.

  1. Only I follows
  2. Only II follows
  3. Both I and II follow
  4. Neither I nor II follows
Answer

A. Only I follows The roses that are flowers cannot be plants, so some roses are not plants.

24. Statements: 1. No doctors is teachers. 2. All teachers are singers. Conclusions: I. Some singers are not doctors. II. No doctors is singers.

  1. Only I follows
  2. Only II follows
  3. Both I and II follow
  4. Neither I nor II follows
Answer

A. Only I follows Every teachers is a singers and no teachers is an doctors, so those singers are not doctors. doctors and singers may still overlap, so II does not follow.

25. Statements: 1. All roses are flowers. 2. All flowers are plants. Conclusions: I. All roses are plants. II. Some plants are roses.

  1. Only II follows
  2. Both I and II follow
  3. Only I follows
  4. Neither I nor II follows
Answer

B. Both I and II follow All roses sit inside flowers, which sits inside plants, so both are true.

26. Statements: 1. All cats are dogs. 2. Some dogs are birds. Conclusions: I. Some cats are birds. II. Some birds are dogs.

  1. Only II follows
  2. Both I and II follow
  3. Only I follows
  4. Neither I nor II follows
Answer

A. Only II follows The birds that are dogs need not be cats, so I does not follow; II is the converse of the second statement.

27. Statements: 1. All cars are buses. 2. All cars are trucks. Conclusions: I. Some buses are trucks. II. All buses are trucks.

  1. Neither I nor II follows
  2. Both I and II follow
  3. Only II follows
  4. Only I follows
Answer

D. Only I follows Every cars is both buses and trucks, so some buses are trucks. Not all buses need be trucks.

28. Statements: 1. No pens is books. 2. No books is bags. Conclusions: I. No pens is bags. II. Some pens are bags.

  1. Only I follows
  2. Either I or II follows
  3. Only II follows
  4. Both I and II follow
Answer

B. Either I or II follows Nothing links pens and bags, but the two conclusions are opposites, so exactly one holds.

29. Statements: 1. No cats is dogs. 2. All dogs are birds. Conclusions: I. Some birds are not cats. II. No cats is birds.

  1. Both I and II follow
  2. Neither I nor II follows
  3. Only I follows
  4. Only II follows
Answer

C. Only I follows Every dogs is a birds and no dogs is an cats, so those birds are not cats. cats and birds may still overlap, so II does not follow.

30. Statements: 1. No phones is laptops. 2. All laptops are tablets. Conclusions: I. Some tablets are not phones. II. No phones is tablets.

  1. Only II follows
  2. Only I follows
  3. Neither I nor II follows
  4. Both I and II follow
Answer

B. Only I follows Every laptops is a tablets and no laptops is an phones, so those tablets are not phones. phones and tablets may still overlap, so II does not follow.

31. Statements: 1. Some chairs are tables. 2. Some tables are desks. Conclusions: I. Some chairs are desks. II. No chairs is desks.

  1. Only II follows
  2. Either I or II follows
  3. Only I follows
  4. Both I and II follow
Answer

B. Either I or II follows Neither is certain alone, but they are opposites covering every case, so one of them must be true.

32. Statements: 1. Some doctors are teachers. 2. No teachers is singers. Conclusions: I. Some doctors are not singers. II. All doctors are singers.

  1. Only I follows
  2. Both I and II follow
  3. Only II follows
  4. Neither I nor II follows
Answer

A. Only I follows The doctors that are teachers cannot be singers, so some doctors are not singers.

33. Statements: 1. All doctors are teachers. 2. Some teachers are singers. Conclusions: I. Some doctors are singers. II. Some singers are teachers.

  1. Both I and II follow
  2. Only II follows
  3. Neither I nor II follows
  4. Only I follows
Answer

B. Only II follows The singers that are teachers need not be doctors, so I does not follow; II is the converse of the second statement.

34. Statements: 1. All roses are flowers. 2. All roses are plants. Conclusions: I. Some flowers are plants. II. All flowers are plants.

  1. Only II follows
  2. Neither I nor II follows
  3. Both I and II follow
  4. Only I follows
Answer

D. Only I follows Every roses is both flowers and plants, so some flowers are plants. Not all flowers need be plants.

35. Statements: 1. Some cats are dogs. 2. Some dogs are birds. Conclusions: I. Some cats are birds. II. No cats is birds.

  1. Only I follows
  2. Both I and II follow
  3. Either I or II follows
  4. Only II follows
Answer

C. Either I or II follows Neither is certain alone, but they are opposites covering every case, so one of them must be true.

36. Statements: 1. No cats is dogs. 2. No dogs is birds. Conclusions: I. No cats is birds. II. Some cats are birds.

  1. Either I or II follows
  2. Only II follows
  3. Only I follows
  4. Both I and II follow
Answer

A. Either I or II follows Nothing links cats and birds, but the two conclusions are opposites, so exactly one holds.

37. Statements: 1. All pens are books. 2. Some books are bags. Conclusions: I. Some pens are bags. II. Some bags are books.

  1. Both I and II follow
  2. Neither I nor II follows
  3. Only II follows
  4. Only I follows
Answer

C. Only II follows The bags that are books need not be pens, so I does not follow; II is the converse of the second statement.

38. Statements: 1. All phones are laptops. 2. Some tablets are not laptops. Conclusions: I. Some tablets are not phones. II. All tablets are phones.

  1. Neither I nor II follows
  2. Only II follows
  3. Both I and II follow
  4. Only I follows
Answer

D. Only I follows The tablets outside laptops are also outside phones (since all phones are inside laptops).

39. Statements: 1. All apples are fruits. 2. All apples are seeds. Conclusions: I. Some fruits are seeds. II. All fruits are seeds.

  1. Only I follows
  2. Both I and II follow
  3. Neither I nor II follows
  4. Only II follows
Answer

A. Only I follows Every apples is both fruits and seeds, so some fruits are seeds. Not all fruits need be seeds.

40. Statements: 1. All cats are dogs. 2. Some birds are not dogs. Conclusions: I. Some birds are not cats. II. All birds are cats.

  1. Only II follows
  2. Neither I nor II follows
  3. Only I follows
  4. Both I and II follow
Answer

C. Only I follows The birds outside dogs are also outside cats (since all cats are inside dogs).

41. Statements: 1. Some phones are laptops. 2. No laptops is tablets. Conclusions: I. Some phones are not tablets. II. All phones are tablets.

  1. Neither I nor II follows
  2. Both I and II follow
  3. Only I follows
  4. Only II follows
Answer

C. Only I follows The phones that are laptops cannot be tablets, so some phones are not tablets.

42. Statements: 1. Some pens are books. 2. Some books are bags. Conclusions: I. Some pens are bags. II. No pens is bags.

  1. Both I and II follow
  2. Either I or II follows
  3. Only II follows
  4. Only I follows
Answer

B. Either I or II follows Neither is certain alone, but they are opposites covering every case, so one of them must be true.

43. Statements: 1. All apples are fruits. 2. All fruits are seeds. Conclusions: I. All apples are seeds. II. Some seeds are apples.

  1. Neither I nor II follows
  2. Only I follows
  3. Both I and II follow
  4. Only II follows
Answer

C. Both I and II follow All apples sit inside fruits, which sits inside seeds, so both are true.

44. Statements: 1. All phones are laptops. 2. No laptops is tablets. Conclusions: I. No phones is tablets. II. Some tablets are phones.

  1. Only I follows
  2. Neither I nor II follows
  3. Only II follows
  4. Both I and II follow
Answer

A. Only I follows Every phones is a laptops and no laptops is a tablets, so no phones is a tablets; II contradicts I.

45. Statements: 1. All chairs are tables. 2. No tables is desks. Conclusions: I. No chairs is desks. II. Some desks are chairs.

  1. Neither I nor II follows
  2. Only I follows
  3. Only II follows
  4. Both I and II follow
Answer

B. Only I follows Every chairs is a tables and no tables is a desks, so no chairs is a desks; II contradicts I.

46. Statements: 1. All pens are books. 2. All books are bags. Conclusions: I. All pens are bags. II. Some bags are pens.

  1. Neither I nor II follows
  2. Only II follows
  3. Only I follows
  4. Both I and II follow
Answer

D. Both I and II follow All pens sit inside books, which sits inside bags, so both are true.

47. Statements: 1. All doctors are teachers. 2. No teachers is singers. Conclusions: I. No doctors is singers. II. Some singers are doctors.

  1. Only I follows
  2. Only II follows
  3. Both I and II follow
  4. Neither I nor II follows
Answer

A. Only I follows Every doctors is a teachers and no teachers is a singers, so no doctors is a singers; II contradicts I.

48. Statements: 1. All cats are dogs. 2. All dogs are birds. Conclusions: I. All cats are birds. II. Some birds are cats.

  1. Only II follows
  2. Both I and II follow
  3. Neither I nor II follows
  4. Only I follows
Answer

B. Both I and II follow All cats sit inside dogs, which sits inside birds, so both are true.

49. Statements: 1. Some phones are laptops. 2. All laptops are tablets. Conclusions: I. Some phones are tablets. II. All tablets are phones.

  1. Both I and II follow
  2. Only II follows
  3. Only I follows
  4. Neither I nor II follows
Answer

C. Only I follows The phones that are laptops are also tablets, so I follows. Nothing says all tablets are phones.

50. Statements: 1. All cats are dogs. 2. No dogs is birds. Conclusions: I. No cats is birds. II. Some birds are cats.

  1. Both I and II follow
  2. Only II follows
  3. Only I follows
  4. Neither I nor II follows
Answer

C. Only I follows Every cats is a dogs and no dogs is a birds, so no cats is a birds; II contradicts I.

Mock test

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