Ch. 21 :- Syllogism : Exercise 2


✦ Directions : In each of the question below are given two statements followed by two conclusions numbered I and II. You have to take the two given statements to be true even if they seem to be at variance from commonly known facts and decide which of the given conclusion(s) logically follow(s) from the two given statements, disregarding commonly known facts.

Given your answer as
(a) if only conclusion I follows
(b) if only conclusion II follows
(c) if either I or II follows
(d) if neither I nor II follows
(e) if both I and II follow

1. Statements :
1.Some dogs are rats.
2.Some rats are lions.
Conclusions :
I. Some dogs are lions.
II. None of the dogs is a lion.

View Answer
Ans.(c)
None of the conclusions is individually valid because I + I = No result. However, both the conclusions make a complementary pair.

2. Statements :
1. All doors are windows.
2. All windows are ventillators.
Conclusions :
I. All ventillators are doors.
II. All windows are doors.

View Answer
Ans.(d)
A + A = A. A correct and valid conclusion is “All doors are ventillators”. Hence, conclusion I does not follow. Conclusion II is immediate inference not correctly drawn from Statement 1.

3. Statements :
1. All pencils are papers.
2. Some papers are books.
Conclusions :
I.Some pencils are books.
II.Some books are papers.

View Answer
Ans.(b)
A + I = No result. Hence, conclusion I does not follow Conclusion II, an immediate inference, follow form Statement 2.

4. Statements :
1. Some cups are bottles.
2.All bottles are glasses.
Conclusions:
I. Some cups are glasses.
II. Some glasses are bottles.

View Answer
Ans.(e)
Both the conclusions follow.

5. Statements :
1. Some novels are epics.
2. All epics are dramas.
Conclusions :
I. Some novels are dramas.
II. Some epics are not novels.

View Answer
Ans.(a)
I + A = I. Hence, Conclusion I follows. Conclusion II is an immediate inference and does not represent the correct conversion of Statement l.

6. Statements :
1.Some schools are factories.
2. All factories are shops.
Conclusions :
I. All shops are factories.
II. Some shops are schools.

View Answer
Ans.(b)
I + A = I. Hence, conclusion II follows. Conclusion I is immediate inference which does not follow form Statement 2 as per rule of conversion.

7. Statements:
1. All trees are tigers.
2. Some tigers are rocks.
Conclusions :
I. Some trees are rocks.
II. No tree is rock.

View Answer
Ans.(c)
Both the conclusions form a complementary pair, hence either Conclusion I or II follows.

8. Statements :
1. Some hens are cows.
2. All cows are horses.
Conclusions :
I. Some horses are hens.
II. Some hens are horses.

View Answer
Ans.(e)
I + A = I. Hence, “hens are horses”. Again on conversion, we get “Some horses are hens.” There fore both the conclusions follow.

9. Statements :
1. All poets are readers.
2. No reader is wise.
Conclusions :
I. No poet is wise.
II. All readers are poets.

View Answer
Ans.(a)
A + E = E. Hence, Conclusion I follows.

10. Statements :
1. Some chairs are stools.
2. Table is a chair.
Conclusions :
I. Some stools are chairs.
II. Table is not a stool.

View Answer
Ans.(a)
Conclusion I is an immediate inference. Hence, on conversion of Statement I, we get “Some stools are chairs”.

11. Statements :
1. All businessmen are hard working.
2. No hard working men are superstitious.
Conclusions:
I. No businessmen are superstitious.
II. All superstitious are not businessmen.

View Answer
Ans.(e)
A + E = E. Hence, no businessman are superstitious Further, no businessman is superstitious => No superstitious are businessmen. Hence, Proposition O “All superstitious are not businessmen” also must be true.

12. Statements :
1. All windows are doors.
2. No door is a wall.
Conclusions:
I. No window is a wall.
II. No wall is a door.

View Answer
Ans.(e)
A + E = E. Hence, Conclusion I is valid. Conclusion II is an immediate inference and follows from statement I.

13. Statements :
1. All poets are authors.
2. All singers are authors.
Conclusions:
I. All singers are poets.
II. Some authors are not singers.

View Answer
Ans.(d)
Statements have to be aligned as “All poets are authors” and “Some authors are singers”. Now A + I = No result Hence, conclusion I does not follow. Conclusion II is an immediate inference and does not follow.

14. Statements :
1. Some trees are small.
2. All small are plants.
Conclusions:
I. All’plants are small.
II. All small are trees.

View Answer
Ans.(d)
Both the conclusions are immediate inferences. None of the conclusions follows.

15. Statements :
1. All educated people read newspapers.
2. Rahul does not read newspaper.
Conclusions :
I. Rahul is not educated.
II. Reading newspaper is not essential to be educated.

View Answer
Ans.(a)
Clearly, Conclusion I follows.

16. Statements :
1. All plants are goats.
2. No goat is green.
Conclusions:
I. Some plants are green:
II. Those plants which are not goat are green.

View Answer
Ans.(d)
A + E = E, i.e., No plant is green. But this is not our conclusion. Hence, none of the conclusions follows.

17. Statements :
1. Some girls are flowers.
2. Some flowers are books.
Conclusions:
I.’ Some girls are books.
II. No book is a girl.

View Answer
Ans.(c)
I + I = No result. But the conclusions make a complementary pair.

18. Statements :
1. Some pots are belts.
2. No belt is white.
Conclusions:
I. Some pots are white.
II. Some pots are not white.

View Answer
Ans.(b)
1+ E = 0, hence our conclusion would be “Some pots are not white.”

19. Statements :
1. All hill stations have a sunset point.
2. X is a hill-station.
Conclusions:
I. X has a sunset point.
II. Places other than hill stations do not have sunset points.

View Answer
Ans.(a)
A + A = A, hence X has a sunset point.

20. Statements :
1. Some parrots are crows.
2. No crow is green.
Conclusions:
I. No parrot is green.
II. No crow is white.

View Answer
Ans.(d)
I + E = 0, i.e., “Some parrots are not green.” But this conclusion is not given.

21. Statements :
1. All clerks are lazy.
2. Some men are clerks.
Conclusions:
I. All lazy are men.
II. Some men are lazy.

View Answer
Ans.(b)

I + A = I. Some men are clerks + All clerks are lazy =>
“Some men are lazy.”

22. Statements :
1. All goats are wolves.
2. Some wolves are tigers.
Conclusions:
I. Some goats are tigers.
II. Tigers, which are wolves, are not goats.

View Answer
Ans.(d)

A + I = No result.

23. Statements :
1. Some aeroplanes are living beings.
2. Some non-living beings are ghosts.
Conclusions:
I. Some aeroplanes are ghosts.
II. Some aeroplanes are not ghosts.

View Answer
Ans.(c)

No mediate inference can be drawn as there is no middle term. However, one of the two conclusions must be true. Hence, either Conclusion I or II follows.

24. Statements :
1. Some papers are needles.
2. All needles are sharp.
Conclusions:
I. All papers are sharp.
II. All needles are papers.

View Answer
Ans.(d)

I + A = I, i.e., some papers are sharp. But this conclusion is not given.

25. Statements :
1. All bags are cakes.
2. All lamps are cakes.
Conclusions:
I. Some lamps are bags .
II. No lamp is a bag.

View Answer
Ans.(c)

Conclusions make a complementary pair.

26. Statements :
1. Some soldiers are famous.
2. Some soldiers are intelligent.
Conclusions:
I. Some soldiers are either famous or intelligent.
II. Some soldiers are neither famous nor intelligent.

View Answer
Ans.(c)

I+ I= No result. However, any soldier must be either famous or intelligent or none of these. Hence, either of the choices follows.

27. Statements :
1. Some men are educated.
2. Educated persons prefer small families .
Conclusions:
I. All small families are educated.
II. Some men prefer small families.

View Answer
Ans.(b)

I+ A = I,hence some men prefer small families.

28. Statements :
1. All players are tall.
2. Sohan is tall.
Conclusions:
I. Sohan is player.
II. Sohan is not a player.

View Answer
Ans.(c)

Statements need to be alinged as Sohan is tall and Some tall are players. Now A + I = No result. But Sohan will be either a player or a non-player. Hence,either of the two conclusions follows.

29. Statements :
1. All students are boys.
2. No boy is dull.
Conclusions:
I. No student is dull.
II. There are no girls in the class.

View Answer
Ans.(a)

A + E = E.

30. Statements :
1. All scientists are researchers.
2. Some researchers are teachers.
Conclusions:
I. No scientist is a teacher.
II. Some teachers are scientists.

View Answer
Ans.(d)

A + I= No result.

31. Statements :
1. Some authors are teachers.
2. No teacher is a lady.
Conclusions:
I. Some teachers are not ladies.
II. Some ladies are teachers.

View Answer
Ans.(a)

I + E = O. Therefore, some authors are not ladies. But this conclusion is not given. However, “No teacher is lady” => “Some teachers are not ladies”. Hence,conclusion I follows.

32. Statements :
1. No women can vote.
2. Some women are politicians.
Conclusions:
I. Male politicians can vote.
II. Some politicians can vote.

View Answer
Ans.(d)

Statements need to be aligned. some politicians are women and no women can vote. I + E = 0, i.e., some politicians can not vote. Hence, none of the conclusions follows.

33. Statements :
1. All radios are pencils.
2. Some pencils are files.
Conclusions :
I. No radio is a file.
II. Some files are radios.

View Answer
Ans.(c)

A + I = No result. But the conclusions make a complementary pair.

34. Statements :
1. Some machines are racks.
2. All wheels are machines.
Conclusions :
I. Some wheels are racks.
II. Some racks are wheels.

View Answer
Ans.(d)

Statements need to be aligned “All wheels are machines” + “Some machines are racks”, A + I = No result. Hence, none of the conclusions follows.

35. Statements :
1. All roads are poles.
2. No pole is a house.
Conclusions :
I. Some roads are houses.
II. Some houses are poles.

View Answer
Ans.(d)

A + E = E, i.e., “No roads are houses”. But this conclusion is not given. Hence, none of the conclusions follows.