# Ch. 21 :- Syllogism : Exercise 4

1. Statements
1. All bars are coins.
2. Some bars are books.
Conclusions
I. Some books are bars.
II. Some books are coins.
III. Some books are not bars.
IV. Some books are not coins.
(a) Only I follows
(b) I and II follow
(c) Either I or III follows
(d) Either II or IV follows
(e) I and either II or IV follow

Ans.(b)
I is an immediate inference and follows from Statement 2. For mediate inference, statements need to be aligned and reordered as some books are bars + All bars are coins => Some books are coins. Hence, I and II follow.

2. Statements :
1. Some stars are birds.
2. No birds are elephants.
Conclusions :
I. Some stars are not elephants.
II. All stars are elephants.
III. Some elephants are not stars.
IV. All elephants are stars.
(a) Either I or II and either III or IV follow
(b) Only I follows
(c) Either III or IV follows
(d) I and III follow
(e) I and either III or IV follow

Ans.(e)
Some stars are birds + No birds are elephants => Some stars are not elephants (I + E = O). Again III and IV make a complementary pair (O – A type).

3. Statements :
1. No book is a hook.
2. All hooks are birds.
Conclusions :
I. Some birds are not books.
II. Some birds are books.
III. Some books are not birds.
IV. Some books are birds.
(a) Either I or II and either III or IV follow
(b) Either I or II.and III follow
(c) Either III or IV and I follow
(d) I and III follow
(e) Only III follows

Ans.(c)
No book is a hook + All hooks are birds => “Some birds are not books” (E + A = O). Again III and IV make a complementary pair.

4. Statements :
1. Some copies are desks.
2. No desks are pens.
Conclusions :
I. Some copies are pens.
II. Some copies are not pens.
III. Some pens are desks.
IV. Some pens are not desks.
(a) Only II follows
(b) II and III follow
(c) Either I or II follows
(d) II and IV follow
(e) Either III or IV follows

Ans.(d)
I + E = O. Hence, “Some copies are not pens” follows. IV is immediate inference drawn from statement 2.

5. Statements :
1. All books are pens.
2. Some pens are pencils.
Conclusions :
I. Some pens are books.
II. No pens are books.
III. Some books are pencils.
IV. No books are pencils.
(a) I and III follow
(b) Only I follows
(c) Either I or II follows
(d) Either III or IV and I follow
(e) Either I or II and III follow

Ans.(d)
I (Immediate inference) follows from Statement 1. A + I = No result. However, III and IV (I-E) make a complementary pair. Hence, either, of these two follows.

6. Statements
1. No systems are decks.
2. All decks are books.
Conclusions
I. Some systems are books.
II. Some systems are not books.
III. Some books are systems.
IV. Some books are not systems.
(a) Only II follows
(b) Only IV follows
(c) II and IV follow
(d) I and either III or IV follow
(e) Either I or II and IV follow

Ans.(e)
E + A = O* (reversed). Hence, “Some books are not systems” follows. Again I and II make a complementary pair, hence one of these two follows

7. Statements :
1. Some drums are baskets.
Conclusions :
I. All gaskets are drums.
II. Some gaskets are drums.
(a) Either II or IV follows
(b) Either II or I follows
(c) I and II follow
(d) Only II follows
(e) II and III follow

Ans.(e)
I + A = 1. Hence, “Some drums are gaskets” follows. Again III is an immediate inference and “All baskets are gaskets” => “Some gaskets are baskets”

8. Statements :
1. No paper is a graper.
2. All grapers are takers.
Conclusions :
I. Some papers are not takers.
II. Some papers are takers.
III. Some takers are not papers.
IV. All takers are papers.
(a) Either I or II follows
(b) Only I follows
(c) Either III or IV follows
(d) Only III follows
(e) Either I or II and III follow

Ans.(e)
E + A = O 1′ (reversed) => “Some takers are not papers”. Further I and II (I – O) make a complementary pair.

9. Statements :
1. Some tables are chairs.
2. All tables are lawns.
Conclusions :
I. Some chairs are lawns.
II. Some chairs are not lawns.
III. Some tables are lawns.
IV. Some tables are not lawns.
(a) Either I or II follows
(b) Either I or II and III follow
(c) Only II and III follow
(d) II and either III or IV follow
(e) None of the above

Ans.(e)
III is an immediate inference and all tables are lawn => Some tables are lawns. Again some chairs are tables + All tables are lawns => Some chairs are lawns. Hence, only I and III follow. But none of our options contains this. Hence, our option is (e)

10. Statements :
1. Some drops are cops.
2. All cops are docks.
3. No dock is a flop.
Conclusions :
I. Some drops are not flops.
II. Some docks are drops.
III. No cop is a flop.
IV. Some flops are not cops.
(a) I, II and III follow
(b) II, III and IV follow
(c) 1,II and IV follow
(d) I, III and IV follow
(e) All follow

Ans.(e)
All follow

11. Statements
1. Some big are small.
2. No small is large.
3. Some large are tiny.
Conclusions :
I. Some large are not big.
II. No big is large.
III. Some small are not tiny.
IV. Some bigs are not tiny.
(a) Only I follows
(b) Only II follows
(c) Only III follows
(d) Only IV follows
(e) None follows

Ans.(e)
All follow

12. Statements :
1. Some diggers are jokers.
2. All jokers are cute.
Conclusions :
I. Some diggers are cute.
II. No diggers are cute.
III. Some diggers are not cute.
IV. All diggers are cute.
(a) I and III follow
(b) Either II or IV follows
(c) I and either III or IV follow
(d) Either I or III follows
(e) None of the above

Ans.(c)
I + A = I. Hence, only “Some diggers are cute” follows III and IV make a complementary pair, hence either of these two should be true.

13. Statements :
1. Some barbers are painters.
2. No painters are watches.
Conclusions :
I. Some barbers are not watches.
II. Some barbers are watches.
III. Some watches are not barbers.
IV. Some watches are barbers.
(a) Only I and III follow
(b) Only I follows
(c) Either I or II and III follow
(d) Either III or IV and I follow
(e) Either I or II and either III or IV follow

Ans.(d)
I + E = O => “Some barbers are not watches”. II and IV make a complementary pair.

14. Statements :
1. Some blankets are pillows.
2. All pillows are books.
Conclusions :
I. Some books are blankets.
II. Some books are pillows.
III. No book is a pillow.
IV. Some blankets are not books.
(a) Only I and IV follow
(b) Only I and II follow
(c) I and either II or III follow
(d) Either I or IV and II follow
(e) Either I or IV or II or III follows

Ans.(b)
I + A = I => Some blankets are books which again implies, “some books are blankets” hence I follows Again “All pillows are books” => Some books are pillows. Hence, II follows.

15. Statements :
1. No girl is an Indian.
2. No American is an Indian.
Conclusions :
I. Some girls are Americans.
II. Some girls are not Americans.
III. All girls are Americans.
IV. No girls are Americans.
(a) Only II follows
(b) Only IV follows
(c) Either I or II follows
(d) Either III or IV follows
(e) None of these

Ans.(c)
E + E = No result. However, I and II, I and N, II and III make complementary pairs. But in option, only I and II is given. Hence, either I or II follows.

16. Statements :
1. No student is decent.
2. Some decent are bags.
3. All bags are roses.
Conclusions :
I. Some bags are not students.
II. All bags are students.
III. Some decents are roses.
IV. All roses are decent.
(a) Only.I follows
(b) Either I or II follows
(c) Only III follows
(d) Either I or II, and III follow
(e) I and III follow

Ans.(e)
No student is decent + Some decent are bags => Some bags are not students (E + I = O* reversed). Hence I follows. Again, I + A = I => Some decent are bags + all bags are roses => Some decent are roses. Hence, I and III follow.

17. Statements
1. Some birds are stones.
2. Some tigers are birds.
3. All stones are grapes.
Conclusions :
I. Some stones are birds.
II. Some stones are not birds.
III. Some grapes are birds.
IV. Some tigers are stones.
(a) I, II and III follow
(b) I, III and IV follow
(c) Either I or II and III follow
(d) I and III follow
(e) None of the above

Ans.(d)
I is an immediate inference and some birds are stones => Some stones are birds. Hence, Conclusion I follow Again I + A = I => Some birds are grapes which can be converted as some grapes are birds. Hence, Conclusion III follows.

18. Statements :
1. Many bucks are ducks.
2. All trucks are ducks.
Conclusions :
I. Some ducks are not bucks.
II. Some bucks are trucks.
III. Some ducks are trucks.
IV. All ducks are trucks.
(a) Only I follows
(b) Only II and III follow
(c) Only III follows
(d) Only IV follows
(e) Only III and IV follow

Ans.(c)
Statements need to be aligned as “All trucks are ducks” + “Some ducks are bucks”. A + I = No result. However
conclusion III is an immediate inference and all truck are ducks => Some ducks are trucks

19. Statements :
1. All students are patriots.
2. All Indians are patriots.
Conclusions :
1. Some students are Indians.
II. Some Indians are students.
III. All Indians are students.
IV. All students are Indians.
(a) Only I and III follow
(b) Only II and IV follow
(c) Only I and II follow
(d) I and II and either III or IV follow
(e) None follows

Ans.(e)
Statements need to be aligned as all Indians are patriots + “Some patriots are students”. A + I = No result Hence, no mediate inference follows.

20. Statements :
1. No Indian is an Asia
2. Some Americans are Indians.
Conclusions :
I. Some Indians are not-Asians.
II. Some Asians are not Americans.
III. Some Americans are not Asians.
IV. All Americans are Asians.
(a) Either III or IV follow
(b) Either I or II follows
(c) I and III follow
(d) Either II or III follows
(e) None of these

Ans.(c)
I + E = O => “Some Americans are not Asians”. Hence III follows. I is an immediate inference and no Indian is an Asian => Some Indians are not Asians. Hence conclusion I and III follow.

21. Statements :
1. Some carts are darts.
2. No smarts are carts.
Conclusions :
I. Some darts are not smarts.
II. All darts are smarts.
III. Some smarts are not darts.
IV. All smarts are darts.
(a) I and III follow
(b) Only I follows
(c) Only III follows
(d) I and either III or IV follow
(e) III and either I or II follow

Ans.(d)
No smarts are carts + Some carts are darts => S darts are not smarts. E + I = O* (reversed). Again Conclusion III and N make a complementary pair.

22. Statements :
1. Some boys are girls.
2. All girls are cute.
Conclusions :
I. Some boys are cute.
II. No boys. are cute.
III. Some cute are girls.
IV. No cute.are girls.
(a) Only I follows Only III follows
(c) Either I or II follows
(d) Either III or IV follows
(e) I and III follow

Ans.(e)
I + A = I => “Some boys are cute.” Hence, Conclusion follows. Again Conclusion III is an immediate inference and “All girls are cute” => “Some cute are girls”.

23. Statements :
1. All blondes are beautiful.
2. All brunnettes are beautiful.
3. All brunnettes are cute.
Conclusions :
I. Some cute are beautiful.
II. Some blondes are cute.
III. Some blondes are brunnettes.
IV. Some brunnettes are not cute.
(a) Only I follows
(b) Only II follows
(c) Only III follows
(d) either II or III follows
(e) I, II and ,III follow

Ans.(a)
“All brunnettes are cute” => “Some cute are brunnettes”, And, I + A = I => “Some cute are brunnettes” + “All brunnettes are beautiful” => “Some cute are beautiful”. Hence, Conclusion I follows.

24. Statements :
1. Some boxes are chocolates
2. Some tables are desks.
3. No box is a desk.
Conclusions :
I. Some chocolates are desks.
II. Some chocolates are not desks.
III. Some tables are boxes.
IV. Some tables are not boxes.
(a) Only I follows
(b) Either I or I, and either
(c) II and N follow
(d) Any three of the above follow
(e) None of the above

Ans.(c)
Some boxes are chocolates => Some chocolates are boxes. Now, Some chocolates are boxes + No box is a desk => Some chocolates are not a desks. Therefore follows. (I + E = O). Again, No box is a deskes No desk is a box. Now, Some tables are desks + No desk is a box => Some tables are not boxes (I + E = O). Hence, IV also follow.

25. Statements :
1. Only red are blues.
2. All reds are yellows.
Conclusions :
I. Some blues are yellows.
II. No blues are yellows.
III. Some yellows are reds.
IV. Some yellows are not reds.
(a) Only I follows
(b) Only III follows
(c) Either I or II follows
(d) Either III or IV follows
(e) I and III follows

Ans.(e)
Only red are blues => All red are blues => Some blues are red. Now, some blues are red + All reds are yellows => Some blues are yellows. And, all reds are yellows => Some yellows are reds. Hence, Conclusions 1 and III follow.

26. Statements :
1. Some songs are throngs.
2. Some throngs are longs.
Conclusions :
I. Some songs are longs.
II. No songs are longs.
III. Only longs are songs.
IV. Only songs are longs.
(a) Only I follows
(b) Only III follows
(c) Either I or II follows
(d) Either III or IV follows
(e) Either I or II and either III or IV follow

Ans.(c)
I + I = No result. However, I and II make a complementary pair. Hence, either I or II follows.

27. Statements :
1. No killer is a sweater.
2. No jacket is a sweater.
3. Some jackets are roses.
Conclusions :
I. Some roses are sweaters.
II. Some roses are not sweaters.
III. No killer is a jacket.
IV. Some jackets are killers.
(a) Either I or II and III follow
(b) Either III or IV and II follow
(c) Either II or III follows
(d) Either I or II and either III or IV follow
(e) None of the above

Ans.(b)
Some jackets are roses. => Some roses are jackets. Now some roses are jackets + No jacket is a sweater => Some roses are not sweaters (I + E = O). Hence, II follows. III and IV make a complementary pair, hence either III or IV follows.

28. Statements :
1. Some books are helmets.
2. Only copies are helmets.
Conclusions :
I. Some books are copies.
II. All helmets are copies.
III. All copies are helmets.
IV. Some copies are not helmets.
(a) I and II follow
(b) II and III follow
(c) I and III follow
(d) I, II and either III or IV follow
(e) None of the above

Ans.(e)
The proposition beginning with ‘only’ is called exclusive proposition and it can be converted into an A-type proposition. Only copies are helmets => All helmets are copies. Now some books are helmets + All helmets are copies => Some books are copies (I + A = I). Hence, I and II follow. Moreover, III and IV make a complementary pair.

29. Statements :
1. Some States are capitals.
2. No pens are capitals.
Conclusions :
I. Some States are not pens.
II. All States are pens.
III. Some pens are not States.
IV. All pens are States.
(a) Only I follows
(b) Only III follows
(c) Either I or II follows
(d) Either III or IV and I follow
(e) Only I and III follow

Ans.(d)
Some States are capitals + No capitals are pen => Some states are not pens (I + E = O). Hence, I follows. II, III
and IV are individually invalid. However, III and IV make a complementary pair.

30. Statements :
1. Some desks are tables.
2. All tables are ice-creams.
3. Some ice-creams are straps.
Conclusions:
I. Some tables are ice-creams.
II. Some desks are ice-creams.
III. Some desk are straps.
IV. Some desk are not straps.
(a) I, II and III follow
(b) I, II and IV follow
(c) Only II and III follow
(d) II and either III or IV follow
(e) I, II and either III or IV follow

Ans.(e)
I, II follows and III and IV make a complementary pair, hence either III or IV follows.

31. Statements :
1. Some barbers are painters.
2. No painters are watches.
Conclusions :
I. Some barbers are not watches.
II. Some barbers are watches.
III. Some watches are not barbers.
IV. Some watches are barbers.
(a) Only I and III follow
(b) Only I follows
(c) Either I or II and III follow
(d) Either III or IV and I follow
(e) Either I or II and either III or IV follow

Ans.(d)
I + E = O => Some barbers are not watches. Hence, I follows. Conclusions III and IV make a complementary pair, hence, either of these two should be valid.

32. Statements :
1. No systems are decks.
2. All decks are books.
Conclusions :
I. Some systems are books.
II. Some systems are not books.
III. Some books are systems.
IV. Some books are not systems.
(a) Only II follows
(b) Only IV follows
(c) II and IV follow
(d) Only I and either III or IV follow
(e) Either l I or II and IV follow

Ans.(e)
No systems are decks + All desks are books => Some books are not systems. Hence, IV follows (E + A = O*). Moreover, I and II make a complementary pair

33. Statements :
1. No book is a hook.
2. All hooks are birds.
Conclusions :
I. Some birds are not books.
II. Some birds are books.
III. Some books are not birds.
IV. Some books are birds.
(a) Either I or II and either III or IV follow
(b) Either I or II and III follow
(c) Either III or IV and I follow
(d) Only I and III follow
(e) Only III follows

Ans.(c)
No book is a hook + All hooks are birds = Some birds are not books (E + A = O*). Hence, I follows. III and IV make a complementary pair.

34. Statements :
1. Some bricks are not sockets.
2. No socket is a pouch.
Conclusions :
I. No brick is a pouch.
II. Some bricks are not pouches.
III. Some sockets are bricks.
IV. No socket is a brick.
(a) Only either III or IV follows
(b) Only II and III follow
(c) Only I and III follow
(d) All follow
(e) None follows

Ans.(a)
O + E = No result. Hence, no conclusion follows. Moreover, III and IV make a complementary pair, hence either III or IV should follow.

35. Statements :
1. No pen is a pencil.
2. All pencils are streets.
Conclusions:
I. No pen is a street.
II. No street is a pen.
III. Some streets are not pens.
IV. Some pens are not streets.
(a) Only I follows
(b) Only II follows
(c) Only III follows
(d) I, II and IV follow
(e) I, II and III follow

Ans.(c)
E + A = O* (reversed) => Some streets are not pens. Hence, only III follows.

36. Statements :
1. No Indian is an Asian.
2. Some Americans are Indians.
Conclusions :
I. Some Indians are not Asians.
II. Some Asians are not Americans.
III. Some Americans are not Asians.
IV. All Americans are Asians.
(a) Either III or IV follows
(b) Either I or II follows
(c) Only I and III follow
(d) Either II or III follows
(e) None of these

Ans.(c)
I + E = I => Some Americans are not Asians. Hence, III follows. I is an immediate inference which follows from Statement 1

37. Statements :
1. Some girls are brunettes.
2. No brunette is wicked.
Conclusions :
I. Some brunettes are girls.
II. Some wicked are girls.
III. Some girls are not wicked.
IV. All wicked are girls.
(a) Only I follows
(b) Either II or III follows
(c) Only I and III follow
(d) Only I and II follow
(e) None of these