Ch. 21 :- Syllogism : Exercise 3


✦ 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. Most crops are machines.
2. Some machines are fools.
Conclusions :
I. Some fools are machines.
II. Some crops are fools.

View Answer
Ans.(a)
“Some machines are fools” => “Some fools are machines”.

2. Statements :
1. All trucks fly.
2. Some scooters fly.
Conclusions :
I. All trucks are scooters.
II. Some scooters do not fly.

View Answer
Ans.(d)
Statements need to be aligned “All trucks fly and some flying objects are scooters”. A + I = No result. Hence, none of the conclusions follows.

3. Statements :
1. All cakes are ice-creams.
2. All ice-creams are toffees.
Conclusions :
I. All cakes are toffees.
II. All toffees are ice-creams.

View Answer
Ans.(a)
A + A = A. Hence, conclusion would be “All cakes are toffees.” Conclusion I follows.

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

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

5. Statements :
1. Some pearls are gems.
2. Some gems are ornaments.
Conclusions :
I. Some gems are pearls.
II. Some ornaments are gems.

View Answer
Ans.(e)
Both the conclusions are immediate inferences. Both follow.

6. Statements :
1. All cars are tables.
2. Some children are tables.
Conclusions :
I. Some cars are children.
II. Some children are cars.

View Answer
Ans.(d)
Statements need to be aligned. “All cars are tables” + “Some tables are children”. A + I = No result. Hence. none follows.

7. Statements :
1. All horses are bullocks.
2. All bullocks are goats.
Conclusions :
I. All horses are goats.
II. All goats are horses.

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

8. Statements :
1. Some books are pencils.
2. Some pencils are pens.
Conclusions :
I. Some books are pens.
II. Some pens are books.

View Answer
Ans.(d)
I + I = No result.

9. Statements :
1. All trays are erasers.
2. All pens are erasers.
Conclusions :
I. All trays are pens.
II. Some pens are trays.

View Answer
Ans.(d)
Statements need to be aligned as all trays are erasers and some erasers are pens. A + I= No result. Hence none of the conclusions follows.

10. Statements :
1. Some chalks are wires.
2. Some wires are frames.
Conclusions :
I. Some chalks are frames.
II. Some frames are chalks.

View Answer
Ans.(d)
I + I = No conclusion. Hence, none of the conclusions follows.

11. Statements :
1. Some pastries are toffees.
2. All toffees are chocolates.
Conclusions :
I. Some chocolates are toffees.
II. Some toffees are not pastries.

View Answer
Ans.(a)
“All toffees are chocolates” => “Some chocolates are toffees”. Hence, Conclusion I, being immediate inference, follows.

12. Statements :
1. All dogs are rats.
2. Some rats are lizards.
Conclusions :
I. Some. dogs are lizards.
II. Some lizards are dogs.

View Answer
Ans.(d)
A + I = No result. Hence, none of the conclusions follows.

13. Statements :
1. All lawyers are cheats.
2. Some women are lawyers.
Conclusions :
I. Some women are cheats.
II. All cheats are women.

View Answer
Ans.(a)
Statements need to be aligned. Some women are lawyers and all lawyers are cheats I + A = I. Hence, some women are cheats.

14. Statements :
1. All readers are teachers.
2. All writers are teachers.
Conclusions :
I. Some teachers are writers.
II. Some writers are readers.

View Answer
Ans.(a)
Statements need to be aligned. “All readers are teachers” and “Some teachers are writers”. A + I = O result. Hence, Conclusion II does not follow. Conclusion I is an immediate inference drawn from Statement 2. Hence, it follows

15. Statements :
1. All young girls are modem.
2. No modern men are superstitious.
Conclusions :
I. No girls are superstitious.
II. No young men are superstitious.

View Answer
Ans.(d)
A + E = E. Hence, conclusion “No young girls are superstitious” follows. But the conclusion is “no girls are superstitious”. Hence, none of the conclusions follows.

16. Statements :
1. Some trees are houses.
2. Biscuit is a tree.
Conclusions :
I. Biscuit is not a tree.
II. Some houses are trees.

View Answer
Ans.(b)
“Some trees are houses’t => “Some houses are trees”.

17. Statements :
1. Some children are adults.
2. Some adults are old.
Conclusions :
I. Some children are not old.
II. Some adults are not old.

View Answer
Ans.(d)
I + I = No result. Hence, none of the conclusions follows.

✦ Directions : In each of the question below, there are two or three Statements given followed by four Conclusions numbered I, II, III and N. You have to take the given statements to be true even if they seem to be at variance with commonly known facts and then decide which of the given conclusion(s) logically follow(s) from the given statements.

18. Statements :
1. Some singers are rockers.
2. All rockers are westerners.
Conclusions :
I. Some rockers are singers.
II. Some westerners are rockers.
III. Some singers are westerners.
(a) I, II and III follow
(b) I, II and IV follow
(c) II, III and IV follow
(d) I, III and IV follow
(e) All follow

View Answer
Ans.(a)
I and II are immediate inferences and follow from Statements 1 and 2, respectively. I + A = I. Hence, conclusion III follows.

19. Statements :
1. All cats are bulls.
2. Some bulls are dogs.
Conclusions :
I. All bulls are cats.
II. Some cats are dogs.
III. No cats are dogs.
IV. Some bulls are cats.
(a) Only IV follows
(b) Only III follows
(c) Only II follows
(d) IV and II follow
(e) IV and either II or III follows

View Answer
Ans.(e)
A + I = No result. However, Conclusion Iv is immediate inference. And II and III make a complementary pair.

20. Statements :
1. All pigs are elephants.
2. No pigs are bakers.
Conclusions :
I. Some bakers are not pigs.
II. Some pigs are not bakers.
III. Some elephants are not bakers.
IV. Some bakers are not elephants.
(a) I, II and III follow
(b) I, II and IV follow
(c) I, III and IV follow
(d) II, III and IV follow
(e) All follow

View Answer
Ans.(a)
II is an immediate inference drawn from Statement 2. Likewise no pigs are bakers => No bakers are pigs => Some bakers are not pigs. Hence, I follows. Now, all pigs are elephants + No pigs are bakers = I + E = O = Some elephants are not bakers. Hence, III follows.

21. Statements :
1. All nibs are tips.
2. Many nibs are ribs.
Conclusions :
I. Some nibs are tips.
II. Some tips are nibs.
III. All nibs are ribs.
IV. Some nibs are not ribs.
(a) Only I follows
(b) Only II follows
(c) Either II or IV follows
(d) I and II follow
(e) I and II and either III or IV follow

View Answer
Ans.(e)
I and II are immediate inferences drawn from statement 1 and follow. Many nibs are tips = Some ribs are tips. I II and IV makes are complementary pair.

22. Statements :
1. All hunters are punters.
2. Some punters are tigers.
Conclusions :
I. Some hunters are tigers.
II. All tigers are punters.
III. Some punters are hunters.
IV. No punters are hunters.
(a) I and II follow
(b) II and III follow
(c) I and III follow
(d) II and IV follow
(e) None of these

View Answer
Ans.(e)
A + I = No result. Conclusion III follows from Statement 1.

23. Statements :
1. Some boxes are dogs.
2. All dogs are pens.
Conclusions :
I. Some boxes are pens.
II. Some pens are boxes.
III. Some pens are dogs.
IV. All pens are dogs.
(a) I, II and III follow
(b) II, III and IV follow
(c) I, III and IV follow
(d) I, II and IV follow
(e) All follow

View Answer
Ans.(a)
I + A = I => “Some boxes are pens” which again implies “Some pens are boxes”. “Some pens are dogs” is an immediate inference drawn from Statement 2.

24. Statements :
1. All bricks are tricks.
2. Some tricks are bricks.
Conclusions:
I. No brick is a brick.
II. Some bricks are bricks.
III. Some bricks are tricks.
IV. Some tricks are not bricks.
(a) Only II follows
(b) Only II and IV follow
(c) Only II and III follow
(d) Either I or II follows
(e) Either I or II, and III follow

View Answer
Ans.(e)
III is an immediate inference drawn from Statement 2. A + I = No result. However, I & II make a complementary pair of conclusions.

25. Statement
1. Some gardens are wardens.
2. All gardens are locks.
Conclusions:
I. Some locks are not wardens.
II. Some locks are wardens.
III. No lock is a warden.
IV. Some locks are gardens.
(a) Only I follows
(b) Only II and IV follow
(c) Either I or II follows
(d) Either I or II and Iv follow
(e) Either I or II and III follow

View Answer
Ans.(b)
IV is an immediate inference drawn from Statement 2.Some wardens are gardens + All gardens are locks = I + A = I => Some wardens are locks => Some locks are wardens. Hence, conclusion II also follows.

26. Statements :
1. Some charts are darts.
2. All darts are carts.
3. Some carts are smarts.
Conclusions :
I. Some charts are carts.
II. Some carts are darts.
III. Some darts are smarts.
IV. Some smarts are charts.
(a) Only I and III follow
(b) Only II and III follow
(c) I and II follow
(d) I, III and IV follow
(e) None of these

View Answer
Ans.(c)
Some charts are darts + All darts are carts => So e charts are carts (I + A = I). II is an immediate inference drawn from Statement 2.

27. Statements :
1. All boxes are tables.
2. No desks are tables.
3. Some desks are curtains.
Conclusions :
I. No boxes are desks.
II. Some boxes are desks.
III. Some curtains are not boxes.
IV. Some curtains are boxes.
(a) III and either I or II follow
(b) I and either III or IV follow
(c) Either I or II and either III or IV follow
(d) I and III follow
(e) None of the above

View Answer
Ans.(d)
All boxes are tables + No desks are tables => All boxes are tables + No tables are desks (After alignment of statements) => No boxes are desks (A + E = E).Again using the conclusion “No boxes are desks” and the Statement 3, we get “No boxes are desks” + “Some desks are curtains” => No boxes are curtains => No curtains are boxes => Some curtains are not boxes. Hence, I and III follow.

28. Statements :
1. All grasses are brasses.
2. All brasses are wickets,
Conclusions :
I. Some brasses are grasses.
II. Some wickets are grasses.
III. Some grasses are not wickets.
IV. All wickets are brasses.
(a) Only I and II follow
(b) Only II and III follow
(c) Only I and III follow
(d) Only I and IV follow
(e) All follow

View Answer
Ans.(a)
I, being an immediate inference, follows from the Statement 1. “All grasses are brasses” + “All brasses are wickets” => All grasses are wickets => Some wickets are grasses.

29. Statements :
1. All teachers are students.
2. Some students are gypsies.
Conclusions :
I. All teachers are gypsies.
II. some gypsies are teachers.
Ill. Some gypsies are students.
IV. All students are teachers.
(a) Only I follows
(b) Only I, II and III follow
(c) Only III follows
(d) Only II and III follow
(e) None of these

View Answer
Ans.(c)
Only III, being an immediate inference, follows from the Statement 2.

30. Statements:
1. Some greens are teens.
2. All teens are cleans.
Conclusions:
I. All greens are cleans.
II. Some greens are cleans.
III. Some cleans are teens.
IV. All teens are greens.
(a) Only I follows
(b) Only I, II and III follow
(c) All follow
(d) Only II and III follow
(e) None of these

View Answer
Ans.(d)
I + A = I => “Some greens are cleans.” “Some cleans are teens” is an immediate inference drawn from Statement 2. Hence, only II and III follow.

31. Statements :
1. All girls are cute.
2. All cute are westernised.
Conclusions :
I. Some cute are girls.
II. No cute is a girl.
III. Some westernised are girls.
IV. All westernised are girls.
(a) Only I follows
(b) Either I or II follows
(c) Either III or IV follows
(d) Only I and III follow
(e) None of these

View Answer
Ans.(d)
A + A = A => “All girls are westernised” => “Some westernised are girls”. Hence, III follows. I is an immediate inference drawn from Statement 1.

32. Statements :
1. Some biscuits are pens.
2. Some pens are pouches.
Conclusions :
I. Some biscuits are pouches.
II. Some pouches are pens.
III. Some pouches are not pens.
IV. Some biscuits are not pouches.
(a) Only II follows
(b) I and II follow
(c) Either II or III follow
(d) Either I or IV follows
(e) II and either I or IV follow

View Answer
Ans.(e)
II is an immediate inference drawn from Statement 2. I + I = No result. However, I and Iv make a complementary pair

33. Statements :
1. All classes are glasses.
2. All brasses are glasses.
Conclusions :
I. Some classes are brasses.
II. Some brasses are glasses.
III. Some brasses are classes.
IV. Some classes are glasses.
(a) Only I follows
(b) Only II follows
(c) I and II follow
(d) II and IV follow
(e) All follow

View Answer
Ans.(d)
II and IV are immediate inferences, hence follow from the rule of conversion from Statements 2 and 1, respectively.

34. Statements :
1. Some trees are sharks.
2. Some sharks are balloons.
Conclusions :
I. All balloons are sharks.
II. All balloons are trees.
III. Some trees are balloons.
IV. No tree is a balloon .
(a) Only I follows
(b) Only II and III follow
(c) Only either I or III follows
(d) Only either I or IV follows
(e) Only either III or IV follows

View Answer
Ans.(e)
I + I = No result. However, III and IV make a complementary pair. Hence, option (e) follows.

35. Statements :
1. Some snakes are cute.
2. All cute are wicked.
Conclusions :
I. Some cute are snakes.
II. No cute is a snake.
III. Some wicked are snakes.
IV. All wicked are snakes.
(a) Only I follows
(b) Only either I or II follows
(c) Only either III or IV follows
(d) Only I and III follow
(e) None of the above

View Answer
Ans.(d)
I + A = I. Hence, Some snakes are wicked, follows => Some wicked are snakes. Again “Some snakes are cute” => “Some cute are snakes”. Hence, only I and III follow