Ch. 21 :- Syllogism : Exercise 5


✦ Directions : Each of the question below has a few statements, followed by four conclusions numbered I, II, III and IV. You have to consider every given statements as true, even if it does not conform to the well known facts. Read the conclusions and then decide which of the conclusions can be logically derived.

1. Statements :
1. Some toys are pens.
2. Some pens are papers.
3. Some papers are black.
Conclusions :
I. Some toys are black.
II. No pen is black.
III. No toy is black.
IV. Some pens are black.
(a) None of these
(b) Either II or IV
(c) Either I or III and either II or IV
(d) Either I or III
(e) All of these

View Answer
Ans.(c)
Statements 2 and 3 give complimentary pairs of conclusions ‘Some pens are black’ or ‘No pen is black’. Likewise, all the three statements taken together give complimentary pairs “Some toys are black” or “No toy is black”

2. Statements :
1. Some books are copies.
2. All copies are green.
3. Some green are yellow.
Conclusions :
I. All copies are yellow.
II. Some yellow are green.
III. Some copies are yellow.
IV. All green are copies.
(a) Only II
(b) Either III or IV Only
(c) Either II or IV Only
(d) All of these
(e) None of these

View Answer
Ans.(a)
A + I = No conclusions, hence conclusion 1 and II do not follow. conclusion II follows (conversion) from statement 3. Conclusion IV does not follow.

3. Statements :
1. All chairs are tables.
2. No table is a book.
3. All tables are stones.
Conclusions :
I. No chair is a book.
II. No stone is a book.
III. Some stones are book.
IV. All tables are chairs.
(a) Only I
(b) Only I and either II or III
(c) Only I and III
(d) Either II or III
(e) None of the above

View Answer
Ans.(a)
A + E = E, hence conclusion I follows.

4. Statements :
1. All jugs are glasses.
2. All glasses are cups.
3. All jugs are pens.
Conclusions :
I. All pens are jugs.
II. Some glasses are pens.
III. Some cups are pens.
IV. All pens are cups.
(a) None
(b) Only II
(c) Only II and III
(d) Only III and IV
(e) None of these

View Answer
Ans.(c)
Statement I all Jugs are glasses [latex]overset{Conversion}{rightarrow}[/latex] Some glasses are jugs. Now, some glasses are jugs + All jugs are pens (Statement 3) => Some glasses are pens O + A = I). Again, statement 1 + Statement 2 => All jugs are cups conversion .

(A + A = A) [latex]overset{Conversion}{rightarrow}[/latex] Some cups are Jugs. And some
cups are jugs + All jugs are pens (statement 3) => Some
cups are pens ( I + A = I). Hence, Conclusions II and III
follow.

5. Statements :
1. All acs are dcs.
2. Some des are ecs.
3. All ecs are yys.
Conclusions :
I. Some acs are ecs.
II. Some yys are des.
III. No acs is ecs.
IV. All des are acs.
(a) Only I and III
(b) Only II
(c) Only I and II
(d) Only II and either I or ill
(e) None of these

View Answer
Ans.(d)
Statement 2 + Statement 3 => Some yys are des (I + A = I). From Statement 1 and Statement 2. We conclude that either some acs are ecs or no acs is ecs. Hence, option (d) follows

6. Statements :
1. Some newspapers are radios.
2. Some radios are televisions.
3. No television is a magazines.
Conclusions :
I. No newspaper is a magazines.
II. No radio is a magazine.
III. Some radios are not magazines.
IV. Some newspapers are televisions.
(a) Cannot be determined
(b) Only III follows
(c) Either I or II follows
(d) Both I and II follow
(e) None of these

View Answer
Ans.(b)
Statement 2 + Statement 3 => Some radios are not magazines (O + E = O). Hence, III follows.

7. Statements :
1. All crooks are simple.
2. Some simple are intelligent.
3. All intelligent are fools.
Conclusions :
I. Some fools are crooks.
II. No fool is a crook.
III. Some simple are fools.
IV. All intelligent are simple.
(a) None follows
(b) Either I or II follows
(c) III and IV follow
(d)Either I or II and III follow
(e) Only I and II, and either III or IV follow

View Answer
Ans.(d)
Some simple are intelligent + All intelligent are fools => Some simple are fools. Hence III follows. Now, all crooks are simple (Statement 1), + Some simple are fools => Either some fools are crooks or no fool is crook
(complimentary pairs).

8. Statements:
1. Some birds are insects.
2. All birds are butterflies.
3. All insects are snakes.
Conclusions:
I. Some snakes are birds.
II. Some butterflies are insects.
III. Some snake are butterflies.
IV. Some in sects are birds.
(a) None follow
(b) All follow
(c) Only IV follow
(d) Either I or III follow
(e) None of these

View Answer
Ans.(b)
Some birds are insects [latex]overset{Conversion}{rightarrow}[/latex] Some insects are birds, hence IV follows some birds are insects (Statement 1) + All insects are snakes (Statement 3) => some snakes are birds (I + A = I). Now some insects are birds + All birds are butterflies (Statement 2) => Some insects are butterflies [latex]overset{Conversion}{rightarrow}[/latex] Some butterflies are insect + all insects are snakes (Statement 3) => Some butterflies are snakes (I + A = I). Hence, all follow.

9. Statements :
1. All apples are brinjals.
2. All brinjals are lady fingers.
3. Some lady fingers are oranges.
Conclusions:
I. Some oranges are brinjals.
II. All brinjals are apples.
III. Some apples are oranges.
IV. All lady fingers are apples.
(a) None
(b) Either I or III follows
(c) All follow and III follow
(d) Only I
(e) None of these

View Answer
Ans.(a)
None of the conclusions follows.

10. Statements :
1. Some apples are watermelons.
2.All watermelons are fresh.
3. Some potatoes are fresh.
Conclusions :
I. Some apples are fresh.
II.Some potatoes are apples.
III. Some watermelons are potatoes.
IV.Some watermelons are apples.
(a) Only I follows
(b) Only I and II follow
(c) Only I and IV follow
(d) Either II or III and I follow
(e)None of the above

View Answer
Ans.(c)
Some apples are watermelons [latex]overset{Conversion}{rightarrow}[/latex] some watermelons are apples; hence IV follows. Some apples are watermelons + All watermelons are fresh => Some apples are fresh (I + A = I)

11. Statements :
1. All pens are pencils.
2.Some pens are erasers.
3.Some erasers are clips.
Conclusions :
I.Some clips are pens.
II. No clip is a pen.
III.Some erasers are pencils.
IV. No eraser is a pencil.
(a) Only I and II follow
(b) III and either I or II follow
(c) Only III follows
(d) Either I or II, and either III or IV
(e)None of the above

View Answer
Ans.(d)
Conclusions I and II form complementary pairs obtained from statements 2 and 3. Likewise conclusions III and IV are complimentary pairs drawn from all the three statements.

12. Statements :
1. Some books are papers.
2. Some papers are plastic.
3. No plastic is black.
Conclusions :
I. Some papers are not black.
II. All papers are not black.
III. Some papers are black.
IV. Some books are black.
(a) Only I follows
(b) Either II or III follows
(c) Only I and IV follow
(d) Only I, III and IV follow
(e) None of the above

View Answer
Ans.(a)
Some papers are plastic + No plastic is black = Some papers are not black (I + E = O). Hence, (I) follows.

13. Statements:
1. Some doors are windows.
2. All windows are black.
3.Some black are brown.
Conclusions:
I. Some windows are brown.
II. All doors are black.
III. Some doors are black.
IV. No window is brown.
(a) Only III follows
(b) Either I or IV and III follow
(c) Only II follows
(d) Only IV follows
(e) None of the above

View Answer
Ans.(b)
Conclusions I and IV for complementary pair following statements 2 and 3. And I + A = L hence III follows.

14. Statements :
1. All teachers are doctors.
2. All doctors are engineers.
3. All engineers are typists.
Conclusions :
I. Some typists are teachers.
II. All doctors are typists.
III. Some engineers are teachers.
IV. All doctors are teachers.
(a) Only I and II follow
(b) Only I and III follow
(c) Either II or IV follows
(d) Either I or II and III follow
(e) None of the above

View Answer
Ans.(e)
None of the conclusions follows.

15. Statements :
1. Some boys are girls.
2. No men are cycles. 3. All girls are men.
Conclusions :
I. Some boys are men.
II. Some boys are cycles.
III. Some boys are not cycles.
IV. No cycle is girl.
(a) Only I and III follow
(b) Only III and IV follow
(c) Only II and IV follow
(d) Only II, III and IV follow
(e) Only I, III and IV follow

View Answer
Ans.(e)
Some boys are girls + All girls are men => Some boys are men (I + A = I).

Hence, I follows. All girls are men + No men are cycles => No cycle is girl (A + E = E). Hence IV follows. No cycle IS girl [latex]overset{Conversion}{rightarrow}[/latex] No girl is cycle. Now some boys are girls + No girl is cycle = Some boys are not cycle (I + E = O) hence, IV follows.

Hence I, III, and IV follow

16. Statements :
1. Some motors are books.
2. Some scooters are motors.
3. All girls are scooters.
Conclusions :
I. Some girls are motors.
II. Some girls are books.
III. Some scooters are girls.
IV. No girl is a book.
(a) Only I and III follow
(b) Only II and III follow
(c) Only I and II follow
(d) Only I, II and III follow
(e) Either II or IV and III follow.

View Answer
Ans.(e)
All girls are scooters [latex]overset{Conversion}{rightarrow}[/latex] Some scooters are girls”. Hence, III follows II and IV form a complementary pairs drawn from all the three statements.

17. Statements :
1. All books are pens.
2. Some boys are books.
3. No pen is a pencil.
Conclusions :
I. Some pens are boys.
II. Some books are pencils.
III. No book is a pencil.
IV. Some boys are not pencils.
(a) Only I, II and IV follow
(b) Only I, III and IV follow
(c) Either 11 or III and IV follow
(d) Either II or III and I follow
(e) Only I, II and III follow

View Answer
Ans.(b)
Some boys are books + All books are pens => Some boys conversion b All are pens (I + A = I) [latex]overset{Conversion}{rightarrow}[/latex] Some pens are boys all books are pens + No pen is a pencil => No book is pencil
(A + E = E). Some boys are pens + No pen is pencil => Some boys are not pencils (I + E = O). Hence, only Conclusions II, III and IV follow.

18. Statements :
1. Some birds are mangoes.
2. No duck is a parrot.
3. All mangoes are ducks.
Conclusions :
I. Some birds are ducks.
II. Some ducks are mangoes.
III. No parrot is duck.
IV. Some birds are not parrots.
(a) Only I, II and III follow
(b) Only II, III and IV follow
(c) Only I, III and IV follow
(d) All follow
(e) Only I, II and IV follow

View Answer
Ans.(d)
From Statements 1 and 3, we conclude that some birds [latex]overset{Conversion}{rightarrow}[/latex] are ducks (I+ A = I). All mangoes are ducks ) some ducks are mangoes. From Statements 3 and 2 → No parrot is duck (A + E = E). From Statements 1, 2 and 3 → Some birds are not parrots. Hence, all the conclusions follow.

19. Statements :
1. Some cups are pots.
2. Some pots are vessels.
3. All vessels are drums.
Conclusions :
I. Some cups are vessels.
II. Some pots are drums.
III. Some cups are drums.
IV. No pot is drum.
(a) Only I, II and III follow
(b) Only II follows
(c) Either II’ and IV follows
(d) Only I and III follow
(e) Only I, III and either II or IV follow

View Answer
Ans.(b)
Only Conclusion II follows from statements 2 and 3.

20. Statements :
1. Some novels are epics.
2. All epics are dramas.
3. No drama is a book.
Conclusions :
I. Some dramas are novels.
II. No novel is a book.
III. Some novels are not books.
IV. No book is a drama.
(a) All follow
(b) Only I, II and IV follow
(c) Only I, III and IV follow
(d) Either I or IV follows
(e) None of the-above

View Answer
Ans.(c)
Conclusion I, III and IV follow.

✦ Directions for Q. No. 21 to 27 : In each of the questions below are given three statements followed by for 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 from commonly known facts. Read all the conclusions and then decide which of the given conclusion(s) logically follow(s) from the given statements disregarding commonly known facts.

21. Statements :
1. Some dogs are rats.
2. All rats are trees.
3. Some trees are not dogs.
Conclusions :
I. Some trees are dogs.
II. All dogs are trees.
III. All rats are dogs.
IV. No tree is dog.
(a) None follows
(b) Only I follows
(c) Only I and II follow
(d) Only II and III follow
(e) All follow

View Answer
Ans.(b)
Some dogs are rats + All rats are trees => Some dogs are trees (I + A = O) [latex]overset{Conversion}{rightarrow}[/latex] Some trees are dogs.

22. Statements :
1. Some boys are rains.
2. All rains are clouds.
3. Some clouds are cars.
Conclusions :
I. Some clouds are boys.
II. Some cars arc boys.
III. Some cars are rains.
IV. Some rains are boys.
(a) None follows
(b) Only IV follows
(c) Only I follows
(d) Both I and IV follow
(e) All follow

View Answer
Ans.(d)
Some boys are rains + All rains are clouds => Some boys are clouds [latex]overset{Conversion}{rightarrow}[/latex] Some clouds s are boys. Some boys are rains [latex]overset{Conversion}{rightarrow}[/latex] Some rains are boys.Therefore,both (I) and (IV) follow.

23. Statements :
1. All bricks are flowers.
2. Some houses are flowers.
3. All pens are houses.
Conclusions :
I. Some houses are bricks.
II. Some pens are flowers
III. Some flowers are bricks.
IV. No pen is flower.
(a) Only either II or IV and III follow
(b) Only either II or IV and I follow
(c) Only either I or III and IV follow
(d) None follows
(e) All follow

View Answer
Ans.(a)
All bricks are flowers [latex]overset{Conversion}{rightarrow}[/latex] Some flowers are bricks hence conclusion III follows. Again,conclusions (II) and (IV) form a complementary pair of conclusions.

24. Statements :
1. All lions are ducks.
2. No duck is a horse.
3. All horses are fruits.
Conclusions :
I. No lion is a horse.
II. Some fruits are horses.
III. Some ducks are lions.
IV. Some lions are horses.
(a) All follow
(b) Only either I or II and both III and IV follow
(c) Only either I or IV and both II and III follow
(d) Only either I or IV and II follow
(e) None of the above

View Answer
Ans.(e)
None of the options shows the correct choice.

25. Statements :
1. Some mountains are rivers.
2. Some rivers are roads.
3. Some roads are windows.
Conclusions :
I. Some windows are roads.
II. Some rivers are mountains.
III.Some roads are mountains.
IV. Some windows are rivers.
(a) All follow
(b) Only I and II follow
(c) Only III and IV follow
(d) Only I and IV follow
(e) None follows

View Answer
Ans.(b)
Some roads are windows [latex]overset{Conversion}{rightarrow}[/latex] Some windows are roads. Some mountains are rivers [latex]overset{Conversion}{rightarrow}[/latex] some rivers are mountains. Hence, both the conclusions I and II follow.

26. Statements :
1. All tigers are rivers.
2. No river is jungle.
3. Some jungle are goats.
Conclusions :
I. Some tigers are goats.
II. Some rivers are goats.
III.Some goats are tigers.
IV. Some jungle are tigers.
(a) Only II and III follow
(b) None follows
(c) Only III and IV follow
(d) Only II and IV follow
(e) Only I and IV follow

View Answer
Ans.(b)
None of the options follows.

27. Statements :
1. Some cars are windows.
2. Some windows are trees.
3. Some trees are hills.
Conclusions :
I. Some hills are cars.
II. Some trees are cars.
III. Some hills are windows.
IV. No car is a hill.
(a) Only either I or II follows
(b) Only either I or III follows
(c) Only either I or IV follows
(d) Only either II or IV follows
(e) Only either III or IV follows

View Answer
Ans.(c)
Conclusions I and IV make a complementry pairs.

✦ Directions for Q. No. 28 to 32 : In each of the questions below there are three statements followed by three conclusions numbered I, II and III. Read all the conclusions given and then decide which of the given conclusion(s) logically follow(s) from the given statements.

28. Statements :
1. All dogs are birds.
2. Some birds are trees.
3. No house is tree.
Conclusions :
I. Some houses are dogs.
II. Some birds are dogs.
III.Some trees are dogs.
(a) Only I follows
(b) Only III follows
(c) Only II follows
(d) Only II and III follows
(e) None of these

View Answer
Ans.(c)
All dogs are birds [latex]overset{Conversion}{rightarrow}[/latex] Some birds are dogs.

29. Statements :
1. All goats are tigers.
2. Some tigers are horses.
3. All horses are jackals.
Conclusions :
I. Some jackals are tigers.
II. Some jackals are goats.
III. Some . horses are goats.
(a) None follows
(b) Only I follows
(c) Only I and II follow
(d) Only II and III follow
(e) All follow

View Answer
Ans.(b)
Some tigers are horse + All horses are jackals => So tigers are Jackals [latex]overset{Conversion}{rightarrow}[/latex] Some Jackals are tigers (I + A = I).

30. Statements :
1. Some pens are tables.
2. All tables are inks.
3. Some inks are apples.
Conclusions :
I. Some apples are pens.
II. Some apples are tables.
III.Some inks are pens.
(a) None follows
(b) Only I follows
(c) Only II follows
(d) Only III follows
(e) None of these

View Answer
Ans.(d)
Only Conclusion III follows.

31. Statements :
1. All fruits are vegetables.
2. All pens are vegetables.
3. All vegetables are rains.
Conclusions :
I. All fruits are rains.
II. All pens are rains.
III.Some rains are vegetables.
(a) None follows
(b) Only I and II follow
(c) Only II and III follow
(d) Only I and III follow
(e) All follow

View Answer
Ans.(e)
All follow.

32. Statements :
1. Some flowers are skies.
2. Some skies are rooms.
3. Some rooms are windows.
Conclusions :
I. Some windows are skies.
II. Some rooms are flowers.
III.No sky is window.
(a) Only I follows
(b) Only either I or II follow
(c) Only either II or III follows
(d) Only either I or III follows
(e) None of the above

View Answer
Ans.(d)
Conclusions I and III farm a set of complimentry pairs.

✦ Directions for Q. No. 33 to 37 : In each of the questions below are given three statements followed by two conclusions (I) and (II). You have to take the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusion(s) logically follow(s) from given statements disregarding commonly known facts.

Give your answers as
(a) if only conclusion I follows.
(b) if only conclusion II follows.
(c) if either conclusion I or II follows.
(d) if neither conclusion I nor II follows.
(e) if both conclusions I and II follow.

33. Statements :
1. Some bulbs are cones.
2. Some cones are books.
3. All books are lanterns.
Conclusions :
I. Some lanterns are cones.
II. Some lanterns are bulbs.

View Answer
Ans.(a)
Some cones are books + All books are lantern (I + A = I) => Some lanterns are cones. Hence Conclusion I follows.

34. Statements :
1. All pens are jungles.
2. All needles are jungles.
3. All boys are jungles.
Conclusions :
I. Some needles are pens.
II. Some boys are pens.

View Answer
Ans.(d)
None of the conclusions follows.

35. Statements :
1. All stones are tents.
2. Some tents are stones.
3. All stones are walls.
Conclusions :
I. Some walls are stones.
II. Some walls are tents.

View Answer
Ans.(b)
Some tents are stones + All stones are walls => Some tents are walls [latex]overset{Conversion}{rightarrow}[/latex] Some wall are tents (I + A = I).

36. Statements :
1. Some bricks are gates.
2. Some gates are roofs.
3. All tyres are bricks.
Conclusions :
I. Some tyres are gates.
II. No gate is a tyre.

View Answer
Ans.(c)
Complimentary pairs of conclusions follow from statements.

37. Statements :
1. All desks are benches.
2. No bench is a chair.
3. All chairs are roads.
Conclusions :
I. Some roads are chairs.
II. No chair is a desk.

View Answer
Ans.(e)
All chairs are roads [latex]overset{Conversion}{rightarrow}[/latex] Some roads are chairs all
desks are benches No bench is a chair (A + E = E) =>
No desk chair [latex]overset{Conversion}{rightarrow}[/latex] No chair desk is a chair Hence both the conclusions follow.