# Ch-21 :- Syllogism :- Exercise 1

✦ 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.

(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 players are singers.
2. All singers are tall.
Conclusions :
I. Some players are tall.
II. All players are tall.

Ans.(a)
Both the statements are aligned, i.e., predicate of the first is the subject of the second. From the table of mediate inference, we know that I + A = I. Hence, conclusion “Some players are tall” follows.

2. Statements
1. Some hats are caps.
2. Some caps are mats
Conclusions :
I. Some caps are hats.
II. Some mats are caps.

Ans.(e)
Both the conclusions are immediate inferences drawn from Statements 1 and 2 and follow from the rule of conversion.

3. Statements :
1. Some vegetables are fruits.
2. No fruit is black.
Conclusions :
I. Some fruits are vegetables.
II. No vegetable is black.

Ans.(a)
Conclusion (I) is the immediate inference drawn from Statement 1. For mediate inference, I + E = O. Therefore, from the pair of statements, conclusion “Some vegetables are not black” is valid. But this is not our conclusion. Hence, only (I) follows.

4. Statements :
1. Some fools are intelligent.
2. Some intelligent are great
Conclusions :
I. Some fools are great
II. All great are intelligent.

Ans.(d)
Conclusion (II) is an immediate inference drawn from Statement 2 and this is not valid as per rule of conversion. Conclusion (I) is a mediate inference. But as per table of mediate inference, I + I = No result. Hence, none of the conclusions follows.

5. Statements :
1. All stones are water
2. Some water are clean.
Conclusions :
I. Some stones are clean.
II. No stone is clean.

Ans.(c)
Both the conclusions are mediate inferences. We know from table of mediate inference that A + I = No result. However, this conclusion forms the complementary pairs and comply the conditions, i.e., both the conclusions are I – E type and have the same subject and predicate. Hence, either (I) or (II) follows.

6. Statements :
1. All keys are locks.
2. All locks are screws.
Conclusions :
I. All screws are keys
II. Some locks are keys.

Ans.(b)
Conclusion (II) is an immediate inference drawn from Statement 2 and follows as per rule of conversion. Conclusion (I) is mediate inference. A + A = A. Therefore, conclusion would be “All stones are clean.” But our conclusion is “All clean are stones”. Hence, does not follow. Therefore, only conclusion (II) follows.

7. Statements :
1. Some books are pens.
2. No pen is pencil.
Conclusions :
I. Some books are pencils
II. No book is a pencil

Ans.(c)
Both the conclusions are mediate inferences. I + E = O. Therefore, a valid conclusion would be “Some books are not pencils”. But, we do not have this as our options. However, both the conclusions are (I – E) type and make a complementary pair. Hence, either I or II follows.

8. Statements :
1. All dogs are monkeys
2. No monkey is a cat.
Conclusions :
I. No dog is a cat.
II. No cat is a dog.

Ans.(a)
Both the conclusions are mediate inferences. A + E = E. Therefore, a valid conclusion would be “No dog is cat”. We know from the rule of conversion that “No dog is cat” => “No cat is dog.” Hence, both the conclusions
follow.

9. Statements :
1. Some phones are watches.
2. All watches are guns.
Conclusions :
I. All guns are watches
II. Some guns are phones.

Ans.(b)
Conclusion (I) is an immediate inference and does not follow. Conclusion (II) is a mediate inference for which I + A = I. Therefore, the conclusion “Some phones are guns” is valid. However, we know that “Some phones are guns” => “Some guns are phones” as per rule of conversion. Hence, conclusion (II) follows.

10. Statements :
1. All umbrellas are aeroplanes.
2. Some aeroplanes are birds.
Conclusions :
I. Some umbrellas are birds.
II. Some birds are umbrellas.

Ans.(d)
Both the conclusions are mediate inferences. A + I = No result. Therefore, no conclusion can be drawn. Moreover, the pair of conclusion is not a complementary pair. Hence, none of the conclusion follows.

11. Statements :
1. All cars are cats.
2. All fans are cats.
Conclusions :
I. All cars are fans.
II. Some fans are cars.

Ans.(d)
The statements are not aligned. For alignment, second statement “All fans are cats” may be converted as “Some cats are fans”. Now, A + I = No result. Since both the inference are mediate inference, hence no conclusion follows

12. Statements :
1. Some scooters are trucks.
2. All trucks are trains.
Conclusions :
I. Some scooters are trains.
II. No truck is a scooter.

Ans.(a)
Conclusion II is an immediate inference drawn from Statement 1 which does not represent the correct converted form of the statement. Conclusion I is a mediate inference for which I + A = I, i.e., “Some scooters are trains”. Hence, only conclusion I follows.

13. Statements :
1. All pencils are pens.
2. No pen is a book.
Conclusions :
I. No pencil is a book.
II. Some pens are pencils.

Ans.(e)
A + E = E. Hence, conclusion “No pencil is a book” follows. Conclusion II is an immediate inference drawn from Statement 1.

14. Statements :
1. Some rats are rabbits.
2. All rats are mosquitoes.
Conclusions :
I. Some mosquitoes are rabbits.
II. No rabbit is mosquito.

Ans.(a)
Statement needs to be aligned after converting Statement 1 as “Some rabbits are rats”, we have I + A = I. Therefore, conclusion “Some rabbits are mosquitoes” which may be converted as “Some mosquitoes are rabbits”. Hence, conclusion I follows. Conclusion II does not follow.

15. Statements :
1. All fans are cups.
2. All cups are pillows.
Conclusions :
I. All fans are pillows.
II. All pillows are fans.

Ans.(a)
A + A = A. Hence “All fans are pillows” follows.

16. Statements :
1. Roma is brilliant.
2. Roma is a woman.
Conclusions :
I. Women are brilliant.
II. Roma is brilliant because she is a woman.

Ans.(d)
None of the conclusions follows.

17. Statements :
1. Some stones are bricks.
2. Some bricks are trees.
Conclusions :
I. Some stones are trees.
II. Some trees are bricks.

Ans.(b)
I + I = No result. Therefore, conclusion I does not follow. Conclusion II is an immediate inference drawn from Statement 2. Hence, it follows.

18. Statements :
1. Some whites are black.
2. No black is green.
Conclusions :
I. Some whites are green.
II. Some whites are not green.

Ans.(b)
I + E = O. Hence, conclusion would be “Some whites are not green”.

19. Statements :
1. All flowers are stems.
2. All stems are roots.
Conclusions :
I. All roots are flowers.
II. All stems are flowers.

Ans.(d)
A + A = A. Therefore, conclusion should be “All flowers are roots.” Hence, conclusion I does not follow. Conclusion II is an immediate inference and also does not follow.

20. Statements :
1. Some cities are villages.
2. Some towns are villages.
Conclusions :
I. Some cities are towns.
II. No city is a town.

Ans.(c)
None of the conclusions is individually true. But both of them being (I – O) type form complementary pairs. Hence, either of these two is valid.

21. Statements :
1. Some visitors are Indians.
2. Some visitors are Americans.
Conclusions :
I. Some Indians are visitors.
II. All Indians are visitors.

Ans.(a)
Both the conclusions are immediate inferences. Conclusion I represents the correct converted form of Statement 1.

22. Statements :
1. All books are pencils.
2.Some pencils are cycles.
Conclusions :
I. Some cycles are pencils.
II. Some cycles are books.

Ans.(a)
Conclusion I is an immediate inference and follows from statement 2. Conclusion II is a mediate inference for which A + I = No result, hence, it does not follow.

23. Statements :
1.All tigers are ships.
2. Some ships are cupboards.
Conclusions :
I. Some tigers are cupboards.
II. Some cupboards are tigers.

Ans.(d)
A + I = No result. Hence, no conclusion follows.

24. Statements :
1. All pencils are bricks.
2. All bricks are bottles.
Conclusions :
I. All pencils are bottles.
II. All bricks are pencils.

Ans.(a)
A + A = A. Hence, conclusion I follows. Conclusion II is an immediate inference and does not follow.

25. Statements :
1. All tigers are ships.
2. Some ships are cupboards.
Conclusions :
I. Some ships are tigers.
II. Some cupboards are not ships.

Ans.(a)
Both the conclusions are immediate inferences drawn from Statements 1 and 2, respectively. Only Conclusion I is the correct conversion of Statement 1.

26. Statements :
1. Some stones are cups.
2. Some cups are black.
Conclusions :
I. Some blacks are not cups.
II. Some cups are stones.

Ans.(b)
Both the conclusions are immediate inferences. Only Conclusion II is the correct converted form of Statement 1.

27. Statements :
1. Some clips are small.
2. All small are big.
Conclusions :
I. All big are small.
II. All small are clips.

Ans.(d)
None of the conclusions follows.

28. Statements :
1.Some books are toys.
2. No toy is red.
Conclusions :
I. Some books are red.
II. Some toys are books.

Ans.(b)
Conclusion II, being the conversion of Statement 1 follows. For conclusion I, I + E = 0, i.e., a valid conclusion is “Some books are not red”. But our conclusion is “Some books are red”. Hence, it does not follow.

29. Statements :
1. All books are pencils.
2. All pencils are pins.
Conclusions :
I. Some pins are books.
II. No pin is a book.

Ans.(a)
A + A = A. Hence, conclusion I follows.

30. Statements :
1. All papers are files.
2. Some files are pens.
Conclusions :
I. No paper is a pen.
II. Some pens are papers.

Ans.(c)
A + I = No result. Though both the conclusions are individually invalid, yet both of the them form the complementary pairs. Hence, either I or II follows.

31. Statements :
1. All books are papers.
2.All papers are sticks.
Conclusions :
I. Some sticks are books.
II. Some sticks are papers.

Ans.(b)
A + A = A = All books are sticks = Some sticks are books. Hence, Conclusion I follows. Conclusion II is an immediate inference drawn from Statement 2, hence follows.

32. Statements :
1. Some chairs are steels.
2. Some steels are wood.
Conclusions :
I. Some wood are chairs.
II. Some wood are steels.

Ans.(b)
I + I = No result. Hence, conclusion I does not follow. However, conclusion II is an immediate inference drawn from Statement 2. Hence, only Conclusion II follows.

33. Statements :
1.Some bags are hots.
2. All hots are cakes.
Conclusions :
I. All cakes are bags.
II. All bags are cakes.

Ans.(d)
I + A = I. Hence, none of the conclusions follows from the statements.

34. Statements :
1. All pens are cycles.
2. All pigs are cycles.
Conclusions :
I. No pig is pen.
II. Some pigs are pens.