Syllogisms Questions and Answers

Q: In the four options given below, three statements are put together in a specific order. Choose the option which indicates a valid argument, that is when the third statement is a conclusion drawn from the preceding two statements.

The valid argument is CEA.C: A few ones are twos. E: All twos are threes. The ones that are twos are therefore threes, so some ones are threes, which the paper words as A: Many ones are threes. 'Many' and 'a few' are both particular statements here, like 'some'.DEB: from 'All fours are threes' and 'All twos are threes' nothing follows about twos and fours; both are merely inside the threes.ACE: two particular premises ('many ones are threes', 'a few ones are twos') never give a universal conclusion such as 'all twos are threes'.EAC: 'All twos are threes' and 'many ones are threes' only place some ones and all twos among the threes; they need not overlap, so 'a few ones are twos' does not follow.

Q: Statements :Some officers are aspirants.All aspirants are girls.Conclusions :I. All officers are boys.II. Some boys are officers.III. Some boys are aspirants.IV. All aspirants are officers.

The answer is None follows.The statements say that some officers are aspirants and that all aspirants are girls. Together they give only that some officers are girls. They say nothing at all about boys.Conclusion I (all officers are boys) and conclusions II and III (some boys are officers, some boys are aspirants) all bring in 'boys', a term that appears in neither statement, so none of them can follow; III even contradicts the statement that all aspirants are girls. Conclusion IV (all aspirants are officers) reverses 'some officers are aspirants' and does not follow either. So every option claiming that one or more conclusions follow is wrong.

Q: Statements :All globes are moons.All moons are boxes.Conclusions :I. All moons are globes.II. All globes are boxes.III. All boxes are moons.IV. Some boxes are globes.

The answer is Only II and IV follow.If all globes are moons and all moons are boxes, every globe is inside the set of moons, which is inside the set of boxes. So all globes are boxes (conclusion II). And since there are globes, and every one of them is a box, some boxes are globes (conclusion IV), by converting II.Conclusion I (all moons are globes) and conclusion III (all boxes are moons) reverse universal statements, which is not valid: the statements allow moons that are not globes and boxes that are not moons. So the options with I or III, and 'None follows', are wrong.

Q: Statements:(A) Some trees are not sharks.(B) Some sharks are not balloons.Conclusions:I. All sharks are balloons.II. All balloons are trees.III. Some trees are balloons.IV. Some trees are not sharks.

Only IV follows.Conclusion IV, 'Some trees are not sharks', is statement (A) itself, so it follows.The others do not. Statement (B) says some sharks are not balloons, which directly contradicts I, 'All sharks are balloons'. Nothing in the statements links balloons to trees, so neither II ('All balloons are trees') nor III ('Some trees are balloons') can be concluded. Two negative particular statements give no definite conclusion between trees and balloons.I and III do not form an either-or pair, because they are not about the same two terms, so 'Only either I or III follows' is also wrong.

Q: Statements:(A) Some google are cottons.(B) No cottons are pillow.Conclusions:I. Some cottons are google.II. Some google are not pillow.III. Some pillowaregoogle.IV. Some cottons are not pillow.

Only I, II and IV follow.I: 'Some google are cottons' converts to 'Some cottons are google', so I follows.II: the google that are cottons cannot be pillows, because no cottons are pillow. So some google are not pillow, and II follows.IV: 'No cottons are pillow' means every cotton is outside pillow, and since some cottons exist (statement A), some cottons are not pillow. IV follows.III, 'Some pillow are google', does not follow: the statements put no pillow inside google. So any option leaving out II or IV, or including III, is wrong.

Q: Statements:(A) Some gadgets are buffaloes.(B) All buffaloes are witches.Conclusions:I. Some gadgets are witches.II. Some witches are buffaloes.III. All witches are buffaloes.IV. Some buffaloes are witches.

Only I, II and IV follow.I: some gadgets are buffaloes, and all buffaloes are witches, so those gadgets are witches. 'Some gadgets are witches' follows.II and IV: 'All buffaloes are witches' gives 'Some buffaloes are witches' (IV) and, by conversion, 'Some witches are buffaloes' (II). Both follow.III, 'All witches are buffaloes', reverses the universal statement, which is not allowed: there may be witches that are not buffaloes. 'Only I & II' leaves out IV, 'Only I & III' includes III, and II and III are not an either-or pair.

Q: In this question, three Statements are given, followed by three Conclusions numbered I, II and III. Assuming the statements to be true even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.Statements : Some tables are birds.No bird is pen.All pens are hills.Conclusions : I. Some hills are birds.II. No hill is bird.III. Some tables are pens.

The answer is Either conclusion I or II follows.From 'No bird is pen' and 'All pens are hills', nothing definite follows about birds and hills: some hills may or may not be birds. So neither I ('Some hills are birds') nor II ('No hill is bird') follows by itself.But I and II are a complementary pair about the same two terms: one says some hills are birds, the other that none is. Exactly one of them must be true, so the answer is 'either I or II'. Conclusion III ('Some tables are pens') does not follow, because the tables that are birds cannot be pens, and nothing is said about other tables.

Q: Human beings are one among many creatures that inhabit an imagined world. In this imagined world, some creatures are cruel. If in this imagined world, it is given that the statement “Some human beings are not cruel creatures” is FALSE, then which of the following set of statement(s) can be logically inferred with certainty?(i) All human beings are cruel creatures.(ii) Some human beings are cruel creatures.(iii) Some creatures that are cruel are human beings.(iv) No human beings are cruel creatures.

The statements that follow with certainty are (i), (ii) and (iii).If “Some human beings are not cruel creatures” is false, then there is no human being who is not cruel, so all human beings are cruel creatures: statement (i).Human beings exist in this world (they are among its creatures), so if all of them are cruel, then some human beings are cruel (ii), and equally some cruel creatures are human beings (iii), which is (ii) read the other way round.Statement (iv), “No human beings are cruel creatures”, contradicts (i), so any option containing it is wrong. Options listing only (i), or only (i) and (ii), leave out statements that also follow.

Q: Given below are three statements and four conclusions drawn based on the statements.Statement 1: Some engineers are writers.Statement 2: No writer is an actor.Statement 3: All actors are engineers.Conclusion I: Some writers are engineers.Conclusion II: All engineers are actors.Conclusion III: No actor is a writer.Conclusion IV: Some actors are writers.Which one of the following options can be logically inferred?

The correct option is only conclusion I and conclusion III are correct.Conclusion I is the converse of Statement 1: if some engineers are writers, then those same people are writers who are engineers, so some writers are engineers. Conclusion III is the converse of Statement 2: “No writer is an actor” means writers and actors do not overlap at all, so no actor is a writer.Conclusion II does not follow: all actors are engineers, but that does not make all engineers actors. Conclusion IV contradicts Statement 2, so it is false, and the “either III or IV” option is wrong because III is definitely true and IV definitely false, not an either-or pair. Only I is incomplete, since III also follows.

Q: All hill-stations have a lake. Ooty has two lakes.Which of the statement(s) below is/are logically valid and can be inferred from the above sentences?(i) Ooty is not a hill-station.(ii) No hill-station can have more than one lake.

Neither (i) nor (ii) follows.“All hill-stations have a lake” means every hill-station has at least one lake. It sets a minimum, not a maximum, so a hill-station with two lakes still satisfies it.Statement (i) does not follow: having two lakes does not stop Ooty from being a hill-station, and nothing says whether it is one. Statement (ii) does not follow either: the premise never limits a hill-station to one lake. Both rest on reading “a lake” as “exactly one lake”.

Important Instructions

Direction for [ Question No: 1 To 1 ] :

Directions (Q. No. 36) : Read the following statements and solve the question based on these.

A. Many ones are threes.
B. All twos are fours.
C. A few ones are twos.
D. All fours are threes.
E. All twos are threes.

In the four options given below, three statements are put together in a specific order. Choose the option which indicates a valid argument, that is when the third statement is a conclusion drawn from the preceding two statements.

A.DEB
B.ACE
C.CEA
D.EAC

Exam Year(s)

Punjab Civil Service - 2021,

Answer: C

The valid argument is CEA.

C: A few ones are twos. E: All twos are threes. The ones that are twos are therefore threes, so some ones are threes, which the paper words as A: Many ones are threes. 'Many' and 'a few' are both particular statements here, like 'some'.

DEB: from 'All fours are threes' and 'All twos are threes' nothing follows about twos and fours; both are merely inside the threes.
ACE: two particular premises ('many ones are threes', 'a few ones are twos') never give a universal conclusion such as 'all twos are threes'.
EAC: 'All twos are threes' and 'many ones are threes' only place some ones and all twos among the threes; they need not overlap, so 'a few ones are twos' does not follow.

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Direction for [ Question No: 2 To 3 ] :

Directions : In each of the questions below are given two statements followed by four conclusions I, II, III and IV. You have to take the two 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 conclusions logically follows from the two given statements, disregarding the commonly known facts.

Statements :
Some officers are aspirants.
All aspirants are girls.

Conclusions :
I. All officers are boys.
II. Some boys are officers.
III. Some boys are aspirants.
IV. All aspirants are officers.

A.Only I follows
B.Only I, II and III follow
C.All follow
D.None follows

Exam Year(s)

Punjab Civil Service - 2018,

Answer: D

The answer is None follows.

The statements say that some officers are aspirants and that all aspirants are girls. Together they give only that some officers are girls. They say nothing at all about boys.

Conclusion I (all officers are boys) and conclusions II and III (some boys are officers, some boys are aspirants) all bring in 'boys', a term that appears in neither statement, so none of them can follow; III even contradicts the statement that all aspirants are girls. Conclusion IV (all aspirants are officers) reverses 'some officers are aspirants' and does not follow either. So every option claiming that one or more conclusions follow is wrong.

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Statements :
All globes are moons.
All moons are boxes.

Conclusions :
I. All moons are globes.
II. All globes are boxes.
III. All boxes are moons.
IV. Some boxes are globes.

A.Only I and III follow
B.None follows
C.All follow
D.Only II and IV follow

Exam Year(s)

Punjab Civil Service - 2018,

Answer: D

The answer is Only II and IV follow.

If all globes are moons and all moons are boxes, every globe is inside the set of moons, which is inside the set of boxes. So all globes are boxes (conclusion II). And since there are globes, and every one of them is a box, some boxes are globes (conclusion IV), by converting II.

Conclusion I (all moons are globes) and conclusion III (all boxes are moons) reverse universal statements, which is not valid: the statements allow moons that are not globes and boxes that are not moons. So the options with I or III, and 'None follows', are wrong.

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Direction for [ Question No: 4 To 6 ] :

In the question below, there are two statements followed by conclusions numbered I, II, III and IV. 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 conclusions logically follow(s) from the given statements.

Statements:

(A) Some trees are not sharks.
(B) Some sharks are not balloons.

Conclusions:

I. All sharks are balloons.
II. All balloons are trees.
III. Some trees are balloons.
IV. Some trees are not sharks.

A.Only I follows
B.Only II & III follow
C.Only either I or III follows
D.Only IV follows

Exam Year(s)

MP Lab Technician - 2015,

Answer: D

Only IV follows.

Conclusion IV, 'Some trees are not sharks', is statement (A) itself, so it follows.

The others do not. Statement (B) says some sharks are not balloons, which directly contradicts I, 'All sharks are balloons'. Nothing in the statements links balloons to trees, so neither II ('All balloons are trees') nor III ('Some trees are balloons') can be concluded. Two negative particular statements give no definite conclusion between trees and balloons.

I and III do not form an either-or pair, because they are not about the same two terms, so 'Only either I or III follows' is also wrong.

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Statements:

(A) Some google are cottons.
(B) No cottons are pillow.

Conclusions:

I. Some cottons are google.
II. Some google are not pillow.
III. Some pillowaregoogle.
IV. Some cottons are not pillow.

A.Only I and IIIfollows
B.Either I or II follows
C.Either III or IV follows.
D.Only I, II and IV follows

Exam Year(s)

MP Lab Technician - 2015,

Answer: D

Only I, II and IV follow.

I: 'Some google are cottons' converts to 'Some cottons are google', so I follows.

II: the google that are cottons cannot be pillows, because no cottons are pillow. So some google are not pillow, and II follows.

IV: 'No cottons are pillow' means every cotton is outside pillow, and since some cottons exist (statement A), some cottons are not pillow. IV follows.

III, 'Some pillow are google', does not follow: the statements put no pillow inside google. So any option leaving out II or IV, or including III, is wrong.

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Statements:

(A) Some gadgets are buffaloes.
(B) All buffaloes are witches.

Conclusions:

I. Some gadgets are witches.
II. Some witches are buffaloes.
III. All witches are buffaloes.
IV. Some buffaloes are witches.

A.Only I, II and IV follows
B.Either II or III follows
C.Only I & III follow
D.Only I & II follow

Exam Year(s)

MP Lab Technician - 2015,

Answer: A

Only I, II and IV follow.

I: some gadgets are buffaloes, and all buffaloes are witches, so those gadgets are witches. 'Some gadgets are witches' follows.

II and IV: 'All buffaloes are witches' gives 'Some buffaloes are witches' (IV) and, by conversion, 'Some witches are buffaloes' (II). Both follow.

III, 'All witches are buffaloes', reverses the universal statement, which is not allowed: there may be witches that are not buffaloes. 'Only I & II' leaves out IV, 'Only I & III' includes III, and II and III are not an either-or pair.

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In this question, three Statements are given, followed by three Conclusions numbered I, II and III. Assuming the statements to be true even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.

Statements : Some tables are birds.
No bird is pen.
All pens are hills.

Conclusions : I. Some hills are birds.
II. No hill is bird.
III. Some tables are pens.

A.Only conclusion II follows.
B.All conclusions I, II and III follow.
C.Either conclusion I or II follows.
D.Only conclusion I follows.

Exam Year(s)

CBSE Assistant Secretary - 2024,

Answer: C

The answer is Either conclusion I or II follows.

From 'No bird is pen' and 'All pens are hills', nothing definite follows about birds and hills: some hills may or may not be birds. So neither I ('Some hills are birds') nor II ('No hill is bird') follows by itself.

But I and II are a complementary pair about the same two terms: one says some hills are birds, the other that none is. Exactly one of them must be true, so the answer is 'either I or II'. Conclusion III ('Some tables are pens') does not follow, because the tables that are birds cannot be pens, and nothing is said about other tables.

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Human beings are one among many creatures that inhabit an imagined world. In this imagined world, some creatures are cruel. If in this imagined world, it is given that the statement “Some human beings are not cruel creatures” is FALSE, then which of the following set of statement(s) can be logically inferred with certainty?

(i) All human beings are cruel creatures.
(ii) Some human beings are cruel creatures.
(iii) Some creatures that are cruel are human beings.
(iv) No human beings are cruel creatures.

A.only (i)
B.only (iii) and (iv)
C.only (i) and (ii)
D.(i), (ii) and (iii)

Exam Year(s)

GATE AE - 2023,

Answer: D

The statements that follow with certainty are (i), (ii) and (iii).

If “Some human beings are not cruel creatures” is false, then there is no human being who is not cruel, so all human beings are cruel creatures: statement (i).

Human beings exist in this world (they are among its creatures), so if all of them are cruel, then some human beings are cruel (ii), and equally some cruel creatures are human beings (iii), which is (ii) read the other way round.

Statement (iv), “No human beings are cruel creatures”, contradicts (i), so any option containing it is wrong. Options listing only (i), or only (i) and (ii), leave out statements that also follow.

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Given below are three statements and four conclusions drawn based on the statements.

Statement 1: Some engineers are writers.
Statement 2: No writer is an actor.
Statement 3: All actors are engineers.

Conclusion I: Some writers are engineers.
Conclusion II: All engineers are actors.
Conclusion III: No actor is a writer.
Conclusion IV: Some actors are writers.

Which one of the following options can be logically inferred?

A.Only conclusion I is correct
B.Only conclusion II and conclusion III are correct
C.Only conclusion I and conclusion III are correct
D.Either conclusion III or conclusion IV is correct

Exam Year(s)

GATE Chemistry - 2022, GATE AG - 2022,

Answer: C

The correct option is only conclusion I and conclusion III are correct.

Conclusion I is the converse of Statement 1: if some engineers are writers, then those same people are writers who are engineers, so some writers are engineers. Conclusion III is the converse of Statement 2: “No writer is an actor” means writers and actors do not overlap at all, so no actor is a writer.

Conclusion II does not follow: all actors are engineers, but that does not make all engineers actors. Conclusion IV contradicts Statement 2, so it is false, and the “either III or IV” option is wrong because III is definitely true and IV definitely false, not an either-or pair. Only I is incomplete, since III also follows.

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10.

All hill-stations have a lake. Ooty has two lakes.

Which of the statement(s) below is/are logically valid and can be inferred from the above sentences?

(i) Ooty is not a hill-station.
(ii) No hill-station can have more than one lake.

A.(i) only
B.(ii) only
C.both (i) and (ii)
D.neither (i) nor (ii)

Exam Year(s)

GATE CS - 2016,

Answer: D

Neither (i) nor (ii) follows.

“All hill-stations have a lake” means every hill-station has at least one lake. It sets a minimum, not a maximum, so a hill-station with two lakes still satisfies it.

Statement (i) does not follow: having two lakes does not stop Ooty from being a hill-station, and nothing says whether it is one. Statement (ii) does not follow either: the premise never limits a hill-station to one lake. Both rest on reading “a lake” as “exactly one lake”.

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Syllogisms Questions and Answers

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