igp csat paper 2 logical reasoning & analytical ability syllogism

3Syllogism

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The word ‘Syllogism’ is also referred to ‘Logic’. Syllogism is an important section of logical reasoning andhence, a working knowledge of its rules is required on the part of the candidate. Hence, it can be expressed as the‘Science of thought as expressed in language’. The questions based on syllogism can be solved by using Venndiagrams and some rules devised with the help of analytical ability.

With this unique characteristic, this test becomes an instrument of teaching the candidates to follow the rulesand work as per the instructions without an error. Here, only the basic concept and rules, which have a bearingon reasoning faculty could alone help. There are some terminology which are used in syllogism.

Pr op os i t i o nIt is also referred to as ‘Premises’. It is a sentence which asserts that either a part of, or the whole of, one sets

of objects-the set identified by the subject term in the sentence expressing that sentence either is included in, or isexcluded from, another set-the set identified by the predicate term in that sentence.

Types o f Proposi t ionCategorical Proposition There is relationship between the subject and the predicate without any condition.Example : I. All beams are logs.

II. No rod is stick.Hypothetical Proposition: There is relationship between subject and predicate which is asserted

conditionally.Example : I. If it rains he will not come.

II. If he comes, I will accompany him.Disjunctive Proposition In a disjunctive proposition the assertion is of alteration.Example : I. Either he is brave or he is strong.

II. Either he is happy or he cannot take revenge.

Parts o f Proposi t ionIt consists of four parts.

1. Quantifier: In quantifier the words, ‘all’, ‘no’ and ‘some’ are used as they express quantity. ‘All’ and ‘no’ areuniversal quantifiers because they refer to every object in a certain set. And quantifier ‘some’ is a particularquantifier because it refers to at least one existing object in a certain set.

2. Subject: It is the word about which something is said.

Syllogism

CHAPTER 1

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Syllogism


3. Predicate: It is the part of proposition which denotes which is affirmed or denied about the subject.4. Copula: It is the part of proposition which denotes the relation between the subject and predicate.

Example : All boys are brilliant↑ ↑ ↑ ↑Quantifier Subject Copula Predicate

Hence, the standard form of proposition isQuantifier + Subject + Copula + PredicateFour-fold classification of categorical proposition: On the basis of quality and quantity of proposition

we can classify them in four categories. To draw valid inferences it is necessary to have a clear

understanding of the A, E, I, O relationship as given in the table.

Symbol Proposition Quantity Quality

A All A are B Universal AffirmativeE No A is B Universal NegativeI Some A are B Particular AffirmativeO Some A are not B Particular Negative

Rules for Deriving the Conclusions from Two Given Premises

1. Universal affirmative or A-type proposition.

Dogs

Goats

Take an example : All goats are dogs This is A type proposition: We can see it by graphical representation ofthe above proposition we observe that goats are distributed in dogs. Hence. we can conclude that in A typeproposition only subject is distributed.

2. Universal negative or E-type proposition.

Boy Girl

Take an example : No girl is boy In this type of proposition both subject and predicate are denial of eachother. This can also be seen in the diagram representing boy Girl and girl. They have nothing in common.Hence, both subject and predicate are distributed.

3. Particular affirmative or I-type proposition.

Mobile Telephone

Take an example : Some mobiles are telephones. In this type of proposition subject and predicate havesomething in common. This implies that in I-type neither subject nor Mobiles Telephones predicate isdistributed. We can see it graphically as given in figure.






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4. Particular negative or O-type proposition.

Boys Students

Take an example : Some boys are not students. In O-type propositions some of the category represented byboys subject is not students, which means that a section of boys is denied with the entire category of students.It is, therefore, deduced that in O-type proposition only predicate is distributed. On account of differentlogical approach required to be applied for drawing each type of inference, a clear understanding of thisdifference becomes more important.

Rules for Media te InferenceFirst introduced by Aristotle, a syllogism is a deductive argument in which conclusion has to be drawn from

two propositions referred to as premises.Now consider an example.Statement: I. Vinay is a boy. II. All boys are honest.Conclusion I. Vinay is honest.

First two sentences I and II are called propositions and the sentence I is called conclusion. This conclusion isdrawn from above given two propositions.

Types of Questions Asked in the ExaminationThere are mainly two types of questions which may be asked under this

1. When premises are in specified form Here premise is in specified form. Here mainly two propositions aregiven. Propositions may be particular to universal; universal to particular; particular to particular; universalto universal.

2. When premises are in jumbled/mixed form Here at least three or more than three proposition are given.Here pair of two propositions out of them follow as same as in specified form.

Type 1 Premises in Specif ied FormsCase 1: The conclusion does not contain the middle term Middle term is the term common to both the premises

and is denoted by M. Hence, for such case, conclusion does not contain any common term belong to both premises.Example 1

Statement: I. All men are girls.II. Some girls are students.

Conclusions I. All girls are men.II. Some girls are not students.

Solution. Since, both the conclusions I and II contain the middle term ‘girls’ so neither of them can follow.Venn diagram Representation: All possible cases can be drawn by using Venn diagram.

Girls

men

Students

or,

Girls Men Students




Syllogism


By using both representation (a) and (b) it is clear all girls cannot be men as well as (a) shows some girls arestudents, here no man is included but at the same time (b) shows some girls are students have some men are alsostudents as all men are girls. Hence, we cannot deduce conclusion II.

So, neither of them can follow.

Example 2 Statement: I. All mangoes are chairs.

II. Some chairs are tables.Conclusions I. All mangoes are tables.

II. Some tables are mangoes.III. No mango is a table.

Solution. Here, the term chair is common to both the statement and hence, is the middle term. Statement(I) is A type proposition and in A-type proposition, only subject is distributed, hence, chair being the predicate inthe statement (I) is not distributed in the second statement. Thus, none of the conclusions following statementis a valid inference.

Venn diagram representation: All possible cases can be drawn as

Chairs

MangoesTables

or,Chairs

Mangoes

Tables

(i) All mangoes are table-this inference is definitely false neither (a) nor (b) shows this conclusion.(ii) Some tables are mangoes, this inference is uncertain or doubtful.(iii) No mango is a table, this inference is also uncertain or doubtful. Though it can be concluded from the above

discussion that no valid inference can be drawn between mango and table.Case 2: No term can be distributed in the conclusion unless it is distributed in the premises.

If case 1 is compiled with by a pair of statement, it is confirmed that valid mediate inferences can be drawnfrom such pair of statement. But every mediate inference drawn cannot be valid. Therefore, case 2 is applied tocheck as to the conclusions drawn from a pair of statement in which middle term is distributed, is valid.Example 3

Statement: I. Some boys are students.II. All students are teenagers.

Conclusions I. All teenagers are students.II. Some boys are teenagers.

Solution. Statement I is an I-type proposition which distributes neither the subject nor the predicate.Statement II is an A type proposition which distributes the subject ‘students’. Conclusion I is an A-type propositionwhich distributes the subject ‘teenagers’ only.

Since. the term teenagers is distributed in conclusion I without being distributed in the premises. So, conclusionI cannot follow. In second conclusion, where it is asked that some boys are teenagers. But from statement I it isclear that some students are not students. These students may not be teenagers.

Venn diagram representation: All possible cases can be drawn as follows

Boys Students

Teenagers

.




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We have given that all students are teenagers so, its reverse cannot be possible. Hence, conclusion I is false.As we are also given that some boys are students and all students are teenagers. So, some boys which arestudents must be teenagers. Hence, conclusion II follows.

Case 3: If one premises is particular, conclusion is particular. Take an example which explains this caseExample 4

Statement: I. Some boys are thieves.II. All thieves are dacoits.

Conclusions I. Some boys are dacoits.II. All dacoits are boys.

Solution. Since, one premise is particular, the conclusion must be particular. So, conclusion II cannot follow.Venn diagram representation: All possible cases can be drawn as follows

Boys Thieves

Dacoits

Here conclusion I follows but the conclusion II cannot follow.Case 4 If the middle term is distributed twice, the conclusion cannot be universal Take an example which

explains such case.

Example 5Statement: I. All Lotus are flowers.

II. No Lily is a Lotus.Conclusions I. No Lily is flowers.

II. Some Lilies are flowers. Solution. Here, the first premise is an A proposition and so, the middle term ‘Lotus’ forming the subject is

distributed.The second premise is an E proposition and so, the middle term ‘Lotus’ forming the predicate isdistributed. Since, the middle term is distributed twice, so the conclusion cannot be universal.

Venn-diagram representation: All possible cases can be drawn as follows

Flowers

Lotus Lily

Lotus

Lotus

Flowers Flowers

Lily

It is clear from the given Venn-diagrams either conclusion I or II must be followed.Case 5 If both the premises are affirmative, the conclusions must be affirmative. Take an example which

follows such case:

Example 6Statement: I. All gardens are schools.

II. All schools are colleges.Conclusions I. All gardens are colleges.

II. Some gardens are not colleges.




Syllogism


Solution. Since, both the premises are affirmative, the conclusion must be affirmative, so conclusion IIcannot follow.

Venn diagram representation: All possible cases can be drawn as follows.

Gardens

Schools

Colleges

Now, taking conclusion I, it is clear that all gardens are also colleges. But taking conclusion II, we cannot thatderive second conclusion is true. Hence, only the first conclusion must be true.

Case 6 No conclusion follows. There are three types of such cases.(a) If both the premises are particular

Example 7Statement: I. Some cups are spoons.

II. Some spoons are sauccers.Conclusions I. All cups are sauccers.

II. Some sauccers are cups.Solution.Since both the premises are particular, so no definite conclusion follows.Venn diagram representation

CupsSpoons

Sauccers

Cups Sacuccers Spoons

It is clear from both given Venn-diagrams that no conclusion is followed.(b) If both the premises are negative

Example 8Statement: I. No flower is mango.

II. No mango is cherry.Conclusions I. No flower is cherry.

II. Some cherries are mangoes.Solution. Since, both the premises are negative hence, neither conclusion follows.Venn diagram representation: It is clear from both Venn-diagrams that neither conclusion follows.(c) I f the major premise is particular and the minor premise is negativeMajor premise is the predicate of the conclusion and minor premise is the subject of the conclusion.

Example 9Statement: I. Some pubs are cows.

II. No kitten are pubs.




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Conclusions I. No pubs are kitten.II. Some cows are kitten.

Solution. Here, the first premise containing the middle term ‘Kitten’ as the subject is the major premise andthe second premise containing the middle term ‘Kitten’ as the predicate is the minor premise. Since, the majorpremise is particular and the minor premise is negative. So, no conclusion follows.

Venn diagram representation: All possible cases are given

PutsCows

Kitten

Pubs Cows Kitten Pubs

Cows

Kitten

(a) (b) (c)

It is clear from the Venn-diagram representation that conclusion I follows.

Complementary pa ir o f conclusionsIn drawing mediate inferences from given statement, students are required to be more attentive in selecting

complementary pair of conclusion where neither of the conclusions is definitely true but a combination of bothmakes a complementary pair. As we have already discussed in case number 1 that in the statement where middleterm is not distributed, no valid mediate inference can be drawn but there still exists a possibility that acomplementary pair of conclusions follows from the statement.

Example 10

Statements I. Some cameras are radios.II. Some statues are cameras.

Conclusions I. Some ratios are statues.II. No radio is statue.

Solution. Either ‘some radios are statues’ or ‘No radio is statue’ follows, as I and E-type proposition form acomplementary pair.

Venn diagram representation We can draw all possible cases as given below

Radios Cameras

Statues

Radios Cameras Statues

Hence, using both diagrammatical representation we can conclude either some radios are statues or ‘no radio’is statue. Hence, at least one of the conclusions must be true.




Syllogism


Spec ial Cases

FactsCombinations (Conclusion) Conclusion

A + E Either I or II followsE + I Either I or II followsI + O Either I or II followsE + O Either I or II follows

Example 11

Statements I. All vegetables are green.II. Some greens are fruits.

Conclusions I. Some fruits are vegetables.II. No fruit is vegetable.

Solution. Here, conclusion I is particular affirmative and conclusion II is universal negative proposition.Hence, either conclusion I or conclusion II follows.

Alternatives

Green

Vegetables

Fruitor

Vegetables

Fruit

Green

Conclusion: If we follow Venn-diagram (a) then we can say no fruit is vegetable. Conclusion II but if wethat follow Venn diagram (b) then we can say some fruits are vegetables (conclusion I).

Here, either Venn diagram (a) or Venn-diagram (b) is possible. Hence, conclusion I or conclusion II must befollowed.

Minimal Possibi l i t iesWe can represent statements by keeping in mind our conclusions It’ we follow that our two conclusions

belong to special case, then either one of them is true.We can represent minimum possibilities as given directly in the statement, we don’t need to think about

parameters.

Example 12

Statements I. Some fruits are vegetables.II. Some vegetables are junk food.

III. Some junk foods are snacks.Conclusions I. Some junk foods are vegetables.

II. Some junk foods are fruits.Solution. Minimal possibilities

Fruit Vegetables Junk foods Snacks




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It is clear from the above diagrams that only conclusion I follows.Type 2 Mixed/jumbled ProblemsIn such type of problem there is a constitution of mixed problems of universal and particular premises.

Directions (Q. Nos. 13 to 16) In each of the questions given below there are three statements followed bythree conclusions numbered I, II and III, you have to take the given statements to be true even if theyseem to be at variance from commonly known facts. Read all the conclusions and then decide which ofthe given conclusions logically follows from the given statements disregarding commonly known, facts.

Example 13

Statements All halls are tyres.Some tyres are wheels.All wheels are cars.

Conclusions I. Some cars are wheels.II. Some cars are tyres.

III. Some wheels are halls.(a) None follows (b) Only I follows(c) Only I and II follow (d) Only III follows

Solution. (c)Conclusions

Tyres

Halls

Cars

Wheels

I. Some cars are wheels. It can be seen from Venn-diagram.II. Also, some cars are tyres (as shown in Venn-diagram).

III. It is not clear from the Venn-diagram. Hence, only I and II follow.

Example 14

Statements Some pictures are frames.Some frames are idols.All idols are curtains.

Conclusions I. Some curtains are pictures.II. Some curtains are frames.

III. Some idols are frames.(a) Only I and II follow (b) Only II and III follow(c) Only I and III follow (d) All follow

Solution. (b)




Syllogism


Conclusions

Pictures

frames

idolsCurtains

I. Does not follow.II. Follows (clear from the Venn-diagram)

III. Follows (clear from the Venn-diagram)Hence, only II and III follow.

Example 15

Statements Some ice are rings.No ring is paint.Some rings are gold.

Conclusions I. No gold is paint.II. No ice is gold.

III. Some rings are paints.IV. All golds are rings.

(a) Only I and III follow (b) Only I and II follow(c) Only III and IV follow (d) None follows

Solution. (d) Hence, none of the conclusions follows.

Ice Rings

Gold

Paint

Example 16

Statements No candle is bell.Some shoes are bells.All tables are shoes.

Conclusions I. Some tables are bells.II. No table is bell.

III. Some shoes are candles.IV. No shoes are candles.

(a) Only I and IV follow (b) Only I and II follow(c) Only III and IV follow (d) None of these

Solution. (d)

Candles BellsTable

Shoes

Solution. (d) Here conclusion I is particular affirmative and conclusion II is its universal negative. Hence,either conclusion I or II follows. Also conclusion III is particular affirmative and conclusion IV is its universalnegative. Hence, either III or conclusion IV follows. Finally, either conclusion I or II follows and either conclusionIII or conclusion IV follows.




Syllogism


Directions (Q. Nos. 1 to 13) In each question givenbelow are two Statements followed by twoconclusions numbered I and II. You have to takethe two given Statements to be true even if theyseem to be at variance from commonly known factsand decide which of the given conclusions logicallyfollows from the the given two Statements,disregarding commonly known facts.

Give answer as

(a) If only conclusion I follows(b) If only conclusion II follows(c) If neither I nor II follows(d) If both I and II follow1. Statement: I. All jungles are tigers.

II. Some tigers are horses.Conclusions I. Some tigers are jungles.

II. All horses are jungles.2. Statement: I. All birds are tall.

II. Some tall are hens.Conclusions I. Some birds are hens.

II. Some hens are tall.3. Statement: I. All artists are smokers.

II. Some smokers are drinkers.Conclusions I. All smokers are artists.

II. Some drinkers are notsmokers.

4. Statement: I. Some hens are cows.II. All cows are horses.

Conclusions I. Some horses are hens.II. Some hens are horses.

5. Statement: I. All buses are cars.II. Some cars are roads.

Conclusions I. Some cars are buses.II. Some buses are roads.

6. Statement: I. Some pastries are toffees.II. All toffees are chocolates.

Conclusions I. Some chocolates are toffees.II. Some toffees are not pastries..

7. Statement: I. Some players are singers.II. All singers are tall.

Conclusions I. Some players are tall.II. All players are tall.

8. Statement: I. All stones are water.II. Some water are clean.

Conclusions I. Some water are stones.II. All clear are water.

9. Statement: I. Some phones are watches.II. All watches are guns.

Conclusions I. All guns are watches.II. Some guns are phones.

10. Statement: I. All umbrellas are aeroplanes.II. Some aeroplanes are birds.

Conclusions I. Some umbrellas areaeroplanes.

II. All birds are umbrellas.11. Statement: I. Some scooters are trucks.

II. All trucks are trains.Conclusions I. Some scooters are trains.

II. No truck is a scooter.12. Statement: I. All tigers are ships.

II. Some ships are cupboards.Conclusions I. Some ships are tigers.

II. Some cupboards are not ships.13. Statement: I. All books are pencils.

II. Some pencils are cycles.Conclusions I. Some cycles are pencils.

II. Some cycles are books.Directions (Q. Nos. 14 to 24) In each question beloware given two Statements followed by twoconclusions numbered I and II. You have to takethe given two Statements to be true even if theyseem to be at variance from commonly knownfacts. Read the conclusion and then decide whichof the given conclusions logically follows from thegiven two ‘ Statements, disregarding commonlyknown facts.

Give answer as(a) If only conclusion I follows(b) If only conclusion II follows(c) If neither I nor II follows(d) If both I and II follow14. Statement: I. All men are dogs.

II. All dogs are cats.Conclusions I. All men are cats.

II. All cats are men.

EX ER C I S E




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15. Statement: I. All film stars are playbacksingers.

II. All film directors are film stars.Conclusions I. All film directors are playback

singers.II. Some film stars are film

directors.16. Statement: I. All pens are roads.

II. All roads are houses.Conclusions I. All houses are pens.

II. Some houses are pens.17. Statement: I. All huts are mansions.

II. All mansions are temples.Conclusions I. Some temples are huts.

II. Some temples are mansions.18. Statement: I. All water is divine.

II. All temples are divine.Conclusions I. All water is temple.

II. All temples are water19. Statement: I. All cars are cats.

II. All fans are cats.Conclusions I. All cars are fans.

II. Some fans are cars.20. Statement: I. All pens are chalks.

II. All chairs are chalks.Conclusions I. Some pens are chairs.

II. Some chalks are pens.21. Statement: I. All fans are cups.

II. All cups are pillows.Conclusions I. All fans are pillows.

II. All pillows are fans.22. Statement: I. All flowers are stems.

II. All stems are roots.Conclusions I. All roots are flowers.

II. All stems are flowers.23. Statement: I. All pencils are bricks.

II. All bricks are bottles.Conclusions I. All pencils are bottles .

II. All bricks are pencils.24. Statement: I. All pens are cycles.

II. All pigs are cycles.Conclusions I. All cycles are pens.

II. All pigs are pens.Directions (Q. Nos. 25 to 40) In each of the questionbelow are given two Statement: s followed by two

conclusions numbered I and II. You have to takethe two given Statement: s to be true even if theyseem to be at variance from commonly known factsand decide which of the given conclusion (s)logically follow (s) from the two given Statement:s, disregarding commonly known facts. Give youranswer as

(a) If only conclusion or I follows(b) If only conclusion II follows(c) If either I or II follows(d) If both I and II follow25. Statement: I. Some hats are caps.

II. Some caps are mats.Conclusions I. Some caps are hats.

II. Some mats are caps.26. Statement: I. Some fools are intelligent.

II. Some intelligent are great.Conclusions I. Some fools are great.

II. No great is fool.27. Statement: I. Some stones are bricks.

II. Some bricks are trees.Conclusions I. Some stones are trees.

II. Some trees are bricks.28. Statement: I. Some cities are villages.

II. Some towns are villages.Conclusions I. Some cities are towns.

II. No town is city.29. Statement: I. Some visitors are Indians.

II. Some visitors are Americans.Conclusions I. Some Indians are visitors.

II. All Indians are visitors.30. Statement: I. Some adults are boys.

II. Some boys are old.Conclusions I. Some adults are not old.

II. Some boys are not old.31. Statement: I. Some books are tables.

II. Some tables are mirrors.Conclusions I. Some mirrors are books.

II. No book is mirror.32. Statement: I. Some dreams are nights.

II. Some nights are days.Conclusions I. All days are either nights or

dreams.II. Some days are nights.

33. Statement: I. Some papers are pens.II. Some pencils are pens.




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Conclusions I. Some pens are pencils.II. Some pens are papers.

34. Statement: I. Some doctors are fools.II. Some fools are rich.

Conclusions I. Some doctors are rich.II. Some rich are doctors.

35. Statement: I. Some clothes are marbles.II. Some marbles are bags.

Conclusions I. No cloth is bag.II. Some bags are clothes.

36. Statement: I. Some stones are cups.II. Some cups are black.

Conclusions I. No black is cup.II. Some cups are stones.

37. Statement: I. Some pearls are gems.II. Some gems are ornaments.

Conclusions I. Some gems are pearls.II. Some pearls are ornaments.

38. Statement: I. Some girls are flowers.II. Some flowers are books.

Conclusions I. Some girls are books.II. No book is a girl.

39. Statement: I. Some aeroplanes are livingbeings.

II. Some living beings are ghosts.Conclusions I. Some aeroplanes are ghosts.

II. Some aeroplanes are notghosts.

40. Statement: I. Some cups are plates.II. Some plates are jugs.

Conclusions I. Some cups are jugs.II. Some jugs are plates.

Directions (Q. Nos. 41 to 50) In each questionbelow are given two statements followed by twoconclusions numbered I and II.You have to takethe given two statements to be true even if theyseem to be at variance from commonly knownfacts. Read the conclusion and then decide whichof the given conclusions logically follows from thetwo given statements, disregarding known facts.

Give answer as(a) If only conclusion I follows(b) If only conclusion II follows(c) If either conclusion I or II follows(d) If neither I nor II follow

41. Statement: I. All roads are poles.II. No pole is a house.

Conclusions I. Some roads are houses.II. Some houses are poles.

42. Statement: I. All fish are tortoise.II. No tortoise is a crocodile.

Conclusions I. All tortoise is a fish.II. No fish is a crocodile.

43. Statement: I. All windows are doors.II. No door is wall.

Conclusions I. No window is wall.II. All door is window.

44. Statement: I. No gentleman is poor.II. All gentlemen are rich.

Conclusions I. No poor man is rich.II. No rich man is poor.

45. Statement: I. Some books are pens.II. No pen is pencil.

Conclusions I. Some books are pencils.II. No book is pencil.

46. Statement: I. No bat is ball.II. No ball is wicket.

Conclusions I. No bat is wicket.II. All wickets are bats.

47. Statement: I. Most teachers are boys.II. Some boys are students.

Conclusions I. Some students are boys.II. Some teachers are students.

48. Statement: I. Some books are toys.II. No toy is red.

Conclusions I. Some books are red.II. Some toys are books.

49. Statement: I. Some whites are black.II. No black is green.

Conclusions I. Some whites are green.II. Some whites are not green.

50. Statement: I. Some pens are pencils.II. No pencil is fruit.

Conclusions I. Some pens are fruit.II. Some pencils are pens.

Directions (Q. Nos. 51 to 65) In each questionbelow are given two Statements followed by fourconclusions numbered I, II, III and IV. You haveto take the two given statements to be true even ifthey seem to be at variance from commonly known




Syllogism


facts. Read all the conclusions and then decidewhich of the given conclusions logically followsfrom the given two statements, disregardingcommonly known facts.

51. Statement: I. Some doors are mangoes.II. All mangoes are bananas.

Conclusions I. All bananas are mangoes.II. All doors are bananas.

III. Some doors are bananas.IV. Some mangoes are doors.

(a) Only I and II follow(b) None follows(c) All follow(d) Only III and IV follow

52. Statement: I. Some chairs are windows.II. No window is sky.

Conclusions I. No window is chair.II. No chair is window.

III. Some windows are skies.IV. Some chairs are skies.

(a) Either III or IV follows(b) Either II or III follows(c) Either II or IV follows(d) None follows

53. Statement: I. No parrot is crow.II. All crows are bats.

Conclusions I. Some bats are parrots.II. All bats are parrots.

III. Some bats are crows.IV. Some bats are not crows.

(a) Either III or IV follows(b) Only I, II and III follow(c) Only II, III and IV follow(d) Only I and II follow

54. Statement: I. All stars are planets.II. All planets are trees.

Conclusions I. All planets are stars.II. All stars are trees.

III. All trees are plants.IV. Some trees are stars.

(a) Only II and IV follow(b) Only I and II follow(c) None follows(d) All follow

55. Statement: I. Some chairs are shoes.II. Some shoes are sticks.

Conclusions I. Some chairs are sticks.II. No chair is stick.

III. All sticks are shoes.IV. All shoes are chairs.

(a) Either I or II follows(b) Either II or IV follows(c) III follows(d) Only I and II follow

56. Statement: I. All buses are dogs.II. Some dogs are horses.

Conclusions I. Some horses are dogs.II. Some dogs are buses.

III. Some buses are horses.IV. Some horses are not dogs.

(a) Either I or III follows(b) Either II or IV follows(c) Only I and II follow(d) None follow

57. Statement: I. Some tigers are rats.II. Some rats are birds.

Conclusions I. Some rats are tigers.II. Some birds are rats.

III. Some birds are tigers.IV. Some rats are both birds and

tigers.(a) All follow (b) Only I and IV follow(c) Only I and III follow(d) Only II and IV follow

58. Statement: I. Some papers are balls.II. No ball is round.

Conclusions I. Some papers are round.II. Some balls are round.

III. Some papers are not round.IV. Some balls are papers.

(a) Only III follows(b) Only IV follows(c) Either III or IV follows(d) Either I or III and IV follows

59. Statement: I. All maps are roads.II. Some roads are town.

Conclusions I. Some towns are maps.II. Some roads are maps.

III. No town is a map.IV. All towns are roads.

(a) Either I or II follows(b) Either I or III and II follows(c) Only I follows (d) Only IV follows




Syllogism


60. Statement: I. Some trees are pens.II. All pens are pencils.

Conclusions I. All pencils are pens.II. All trees are pens.

III. Some trees are not pens.IV. All pencils are trees.

(a) Only I and II follow(b) Only III and IV follow(c) Only IV follows(d) None of these

61. Statement: I. All papers are bags.II. No bag is green.

Conclusions I. No paper is green.II. Some papers are green.

III. Some green are papers.IV. Some bags are papers.

(a) Either I or II follows(b) Only I and III follow(c) Only I and IV follow(d) None of these

62. Statement: I. All bananas are apples.II. All apples are oranges.

Conclusions I. Some oranges are apples.II. All apples are bananas.

III. Some bananas are notoranges.

IV. Some oranges are bananas.(a) All follow(b) Only I and IV follow(c) Only I and III follow(d) Only I follows

63. Statement: I. Some pens are knives.II. Some knives are horses.

Conclusions I. Some knives are pens.II. Some pens are horses.

III. Some horses are pens.IV. Some horses are knives.

(a) Only II and III follow(b) Only I and IV follow(c) Only IV follows(d) Only I follow

64. Statement: I. No chair is tree.II. All trees are trains.

Conclusions I. No chair is train.II. No train is chair.

III. Some trains are trees.IV. No train is tree.

(a) Only III follows(b) Only III and IV follow(c) Only I and II follow(d) Only II and III follow

65. Statement: I. All buses are roads.II. All roads are rivers.

Conclusions I. All buses are rivers.II. Some roads are buses.

III. Some rivers are roads.IV. Some rivers are buses.

(a) None follows(b) Only I and II follow(c) Only II, III and IV follow(d) All follow

Directions (Q. Nos. 66 to 78) Every question belowhas a few statement, followed by four conclusionsnumbered I, II, III and IV. You have to considerevery given statement as true, even if it goes notconform to the well known facts. Read theconclusions and then decide which of theconclusions can be logically derived.

66. Statement: I. Some toys are pens.II. Some pens are papers.

III. 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 the above(b) Either II or IV(c) Either I or III and either II or IV(d) Either I or IV

67. Statement: I. Some books are copies.II. All copies are green.

III. 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 follows(b) Either III or IV only(c) Either II or IV only(d) All of these

68. Statement: I. All jugs are glasses.II. All glasses are cups.

III. All jugs are pens.




Syllogism


Conclusions I. All pens are jugs.II. Some glasses are pens.

III. Some cups are pens.IV. All pens are cups.

(a) None follows (b) Only II follows(c) II and III Only (d) III and IV only

69. Statement: I. All Acs are Dcs.II. Some Des are Ecs.

III. All Ecs are yys.Conclusions I. Some Acs are Ecs.

II. Some yys are Dcs.III. No Acs is Ecs.IV. All Des are Acs.

(a) I and III only (b) Only II follows(c) I and II only(d) II and either I or III only

70. Statement: I. Some newspapers are radios.II. Some radios are televisions.

III. No television is a magazine.Conclusions I. No newspaper is a magazine.

II. No radio is a magazine.III. Some radios are magazines.IV. Some newspapers are

televisions.(a) None follows(b) Only III follows(c) Either II or III follows(d) Both I and II follow

71. Statement: I. All crooks are simple.II. Some simple are intelligent.

III. All intelligent are fools.Conclusions I. Some fools are crooks.

II. No fool is a crooks.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

72. Statement: I. Some birds are insects.II. All birds are butterflies.

III. All insects are snakes.Conclusions I. Some snakes are birds.

II. Some butterflies are insects.III. Some snakes are butterflies.IV. Some insects are birds.

(a) None follows (b) All follow(c) Only IV follows (d) Either I or III follows

73. Statement: I. All apples are brinjals.II. All brinjals are ladyfingers.

III. Some ladyfingers are oranges.Conclusions I. Some oranges are brinjals.

II. All brinjals are apples.III. Some apples are oranges.IV. All ladyfingers are apples.

(a) None follows(b) Either I or III follows(c) All follow(d) Only I and III follow

74. Statement: I. Some apples are watermelons.II. All watermelons are fresh.

III. 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

75. Statement: I. All pens are pencils.II. Some pens are erasers.

III. 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

76. Statement: I. Some books are papers.II. Some papers are plastic

III. 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




Syllogism


77. Statement: I. Some doors are windows.II. All windows are black.

III. 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

78. Statement: I. All teachers are doctors.II. All doctors are engineers.

III. 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) None of these

ANSWERS

1. (a) 2. (b) 3. (b) 4. (d) 5. (a) 6. (d) 7. (a) 8. (a) 9. (b) 10. (c)11. (a) 12. (d) 13. (a) 14. (a) 15. (d) 16. (b) 17. (d) 18. (c) 19. (c) 20. (b)21. (a) 22. (c) 23. (a) 24. (c) 25. (d) 26. (c) 27. (b) 28. (c) 29. (a) 30. (d)31. (c) 32. (b) 33. (d) 34. (c) 35. (c) 36. (b) 37. (a) 38. (c) 39. (c) 40. (b)41. (d) 42. (b) 43. (a) 44. (c) 45. (c) 46. (d) 47. (a) 48. (b) 49. (c) 50. (b)51. (d) 52. (d) 53. (a) 54. (a) 55. (a) 56. (d) 57. (b) 58. (d) 59. (d). 60. (d)61. (d) 62. (b) 63. (b) 64. (a) 65. (d) 66. (c) 67. (a) 68. (a) 69. (d) 70. (c)71. (d) 72. (b) 73. (a) 74. (c) 75. (d) 76. (b) 77. (b) 78. (d)

EXPLANATIONS

1. Tigers

Jungles Horses

Hence, only I follows.

2.Tall

Birds Hens

Hence, from both Venn-diagram conclusion IIfollows.

3.Smokers

Aritist Drinkers

Hence, conclusion I follows.

4.

Hens Cows

Horses

Hence, both conclusions are true.5.

Cars

Buses

Roads

Roads

Hence, only I follows.6.

Pastries Chocolates

Toffees

Hence, both I and II are true.




Syllogism


7.

Players Singers

Tall

Hence, some players are tall, only I follows.8.

Water

Stones Clean


Phones Watches

Guns

Hence, only II follows.10.

Aeroplanes

Umbrellas Birds

Hence, none follows.11.

Scooters Trucks

Trains


Ships

Tigers Cupboards

Hence, both follow.13.

Pencils

Books Cycles


14.Cats

Dogs

Men

Hence, only I follows.15. Playback Singers

Filmstars

Film Directors

Hence, both I and II follow.

16. Houses

Roads

Pens


Temples

Mansions

Huts

Hence, both I and II follow.18. Divine

Water

Temples or, Water

Divine

Temples

Hence, none follows.




Syllogism


19. Cats

Cars Fans

Cats

Cars

FansOr,


Chalks

Pens Charis

Hence, only II follows.

21. Pillows

Cups

Fans


22. Roots

Stems

Flowers

Hence, neither I nor II follows.

23.Bottles

Bricks

Pencils


24.Cycles

Pens Pigs

Hence, neither I nor II follows.

25.

Hats Caps

Mats

or, Hats

Mats

Caps

Hence, both I and II follows.

26.

Fools Intelligent Great

Hence, eithr I or II follows.

27.

Stones Bricks Trees

Hence, some trees are bicks (II follows).

28.Cities Villages Towns

It is a special case. Hence, either conclusion I orconclusion II follows.Hence, either I or II follows.

29.

Visitors Indian or Visitors Indians

Americans


30.Adults Boys Old

Hence, I and II follow.




Syllogism


31.

Books Tables

Mirrors

Hence, either I or II follows.Aliter It is a special case hence, either conclusionI or conclusion II follows.

32.

Dreams Nights

Days


Papers Pens

Pencisl

Hence, both follow.

34.

Doctors Fools or

Rich

Doctors

Fools

Hence, either I or II follows.Aliter It is a special case. Hence, either canconclusion I or conclusion II follows.

35.

Cloths Marbles Bags

Hence, either I or II follows.Aliter Its conclusions belong to special case.Hence, conclusion I or conclusion II follows.

36.

Stones Cups

Black


37.

Pearls Gems

Ornaments

Hence, I follows.38.

Girls Flowers

Books

Hence, either I or II follows.Aliter It is special case. Hence, either conclusionI or conclusion II follows.

39.

Aeroplanes Living beings

Ghosts

Hence, either I or II follow.Aliter Its conclusions belong to special case.

40.

Cups Plates

Jugs

Hence, II follows.

41. Poles

Roads House


42. Tortoise

Fish Crocodile


43. Doors

Windows Wall

Hence, only I follows




Syllogism


44.Gentleman Poor

Rich

Hence, either I or II follows.Aliter Its conclusions belong to a special case.Hence, either conclusion I or conclusion II follows.

45.

Book Pens Pencil

Hence, either I or II is true.Aliter Its conclusions belong to a special case.Hence, either conclusion I or conclusion II follows.

46.Bat Ball Wicket

Hence, either I nor II follows.

47.

Teachers Boys Students


48.Books Toys Red


49.

Whites Black Green or

Whites

Green Black

Hence, either I or II follows.Aliter Its conclusions belong to a special case.Hence, either conclusions I or conclusion II follows.

50.Pens Pencils Fruits


51.

Doors Mangoes

Bananas

Hence, both III and IV follow.

52.Chairs Windows Sky


Parrot

Bats

Crow

Hence, only III follows.

54. Trees

Planets

Stars

Hence, only II and IV follow.

55.

Chairs Shoes

Sticks

Hence, either I or II follows.Aliter Its conclusions belong to special case.Hence, either conclusion I or conclusion II follows.

56.

Dogs

Buses

Horses

Hence, only I, II and IV follows.57.

Tigers Rats

Birds

Hence, only I and IV follows.




Syllogism


58.

Paper Ball Round

Hence, either I or III and IV follows.Aliter Its conclusions belong to special case.Hence, either conclusion I or conclusion IV follows.

59.

Roads

Maps

Towns

Hence, either I or III and II follows.Aliter Its conclusions belong to special case.Hence, either conclusion I or conclusion III follows.

60.

Trees Pens

Pencils


61. Bags

Green Papers

Hence, either I or II and IV follows.Aliter Its conclusions belong to special case.Hence, either conclusion I or conclusion II follows.

62.Organes

Apples

Bananas

Hence, only I and IV follow.

63.

Pens Knives

Horses

Hence, only I and IV follow.

64.

ChairTrains

Trees or, Chair

Trains

Trees


65.Rivers

Roads

Buses

Hence, all follow.

66.Toys Pens Papers Black

Here special case can be applied for conclusion Iand III also for conclusion II and conclusion IV.Hence, either I or III and II or IV follow.

67.

Books Copies

Green

Yellow

Hence, only II follows.68. Cups

Glasses

Pens

Jugs

Cups

Pens

Glasses

Jugs

Pens

Cups

Glasses

Jugs

or,

or,





Syllogism


69.

ACS

DCS

ECS

YYS

Hence, either I or II and III follows.70.

Newspapers Radios Televisions Magazine

Hence, either II or III follows.

71.Simple

Crooks

Intelligent

Fools

Conclusion I and II follow special case. Hence,either I or conclusion II follow. Also from Venn-diagram conclusion III follows.

72.

Birds

Butterflies

Insects

Snakes

Hence, all follows.

73.Lady fingers

Brinjals

Apples

Orange

None follows.

74.

Apples Watermelon

Fresh

Potatoes

Hence, I and IV follows.

75.Pencils

Pens

ClipsErasers

Hence, either I or II and either III or IV follows.76.

Books Papers Plastic Black

Hence, either II or III follows.

77.

Doors Windows

Black

Brown

Hence, either I or IV and III follows.78.

Typists

Engineers

Doctors

Teachers

Hence, only I, II and III follow.




igp csat paper 2 logical reasoning & analytical ability syllogism

Documents

disjunctive proposition

hypothetical proposition

subject term

o relationship

predicate term

word syllogism

certain set

t i o nit