Syllogisms Questions and Answers

Q: Which of the following statements is/are correct?1. If all jasmines are flowers and some flowers are white, then some jasmines may be white.2. If all rats are mammals and all mammals are animal, then all rats are animals.Select the answer using the codes given below:

Both 1 and 2 are correct.Statement 1: all jasmines are flowers and some flowers are white. The white flowers may or may not include jasmines, so 'some jasmines may be white' is a possibility that the premises allow. A definite 'some jasmines are white' would not follow, but 'may be' does.Statement 2 is a valid chain: all rats are mammals and all mammals are animals, so all rats are animals.So neither statement oversteps its premises, and the answer is both.

Q: Consider the following pairs:1. All roses are flowers : Some flowers are roses2. Some students are athletes : All athletes are students3. No cats are dogs : No dogs are cats.How many of the above pairs are correctly matched?

Only two pairs are correctly matched.Each pair gives a statement and a conclusion drawn by converting it.Pair 1: 'All roses are flowers' converts by limitation to 'Some flowers are roses'. Valid.Pair 2: 'Some students are athletes' converts only to 'Some athletes are students'; it says nothing about all athletes. Invalid.Pair 3: a universal negative converts simply: 'No cats are dogs' means 'No dogs are cats'. Valid.So pairs 1 and 3 match and pair 2 does not.

Q: The question given below contains four arguments of three sentences each. Choose the set in which the third statement is a logical conclusion of the first two.1. All Ts are square; All squares are rectangular; All Ts are rectangular.2. Some fat are elongated; Some elongated things are huge; Some fat are huge.3. Idiots are bumblers; Bumblers fumble; Idiots fumble.4. Water is good for health; Health foods are rare; Water is rare.

The valid sets are 1 and 3.Set 1: all Ts are squares and all squares are rectangular, so all Ts are rectangular. A valid chain.Set 3: idiots are bumblers and bumblers fumble, so idiots fumble. Also a valid chain.Set 2 is invalid: the fat things that are elongated need not be among the elongated things that are huge, so two 'some' premises prove nothing. Set 4 is invalid: water is good for health, but that does not make water a 'health food', and even if it were, 'health foods are rare' would not make water rare. So '4 only' and '1, 2, 3 & 4' are wrong, and '3 only' misses set 1.

Q: Some cricket players are tennis players. All tennis players are hockey players. Which of the following is definitely true ?

The definite conclusion is Some cricket players are hockey players.Some cricket players are tennis players, and every tennis player is a hockey player. So those cricket players who play tennis are certainly hockey players, which means at least some cricket players are hockey players.'All cricket players are hockey players' does not follow, because the cricketers who do not play tennis may or may not play hockey. 'Some cricket players are not hockey players' is only possible, not certain. 'Some tennis players are not hockey players' contradicts the second statement.

Q: If 'No S is P' is a false statement, then which of these statements is necessarily true ?

If 'No S is P' is false, then Some S is P is necessarily true.In traditional logic, 'No S is P' (a universal negative, E) and 'Some S is P' (a particular affirmative, I) are contradictories: exactly one of them is true. So when 'No S is P' is false, 'Some S is P' must be true.'All S is P' may or may not be true: it is possible that only some S are P. 'Some S is not P' is also undetermined, since every S might be P. Only 'Some S is P' follows necessarily, so 'None of the above' is wrong too.

Q: Consider the following argument :"In order to be a teacher, one must graduate from college. All poets are poor. Some Mathematicians are poets. No college graduate is poor." Which one of the following is not a valid conclusion regarding the above argument ?

The conclusion that is not valid is Some teachers are not Mathematicians.From the premises: every teacher is a graduate, no graduate is poor, so no teacher is poor (option c follows). All poets are poor, so no poet is a graduate and hence no poet is a teacher (option d follows). Some mathematicians are poets, and those cannot be teachers, so some mathematicians are not teachers (option a follows).Nothing in the argument says anything about teachers who are not mathematicians; all teachers might be mathematicians who are not poets. So option (b) does not follow.

Q: Consider the given statements to be true even if they seem to be at variance from the commonly known facts. Decide which of the conclusions logically follow the given statements.Statements:Some computers are machines. Some laptops are computers. All desktops are computers.Conclusions:I. Some desktops are machines.II. Some Laptops are desktops.Choose the most appropriate answer from below given options:

The answer is Neither Conclusion I nor II follows.All desktops are computers, but only some computers are machines. The computers that are machines need not include any desktops, so 'Some desktops are machines' is possible but not certain. Conclusion I does not follow.Some laptops are computers and all desktops are computers, but two groups both lying inside 'computers' need not overlap. 'Some laptops are desktops' is likewise only a possibility, so Conclusion II does not follow either.

Q: Which conclusion would follow on the basis of the given statements ?Statements : (a) All circles are triangles. (b) No triangle is rectangle. (c) All squares are rectangles.Conclusions : (i) Some triangles are squares. (ii) Some triangles are circles. (iii) Some squares are rectangles. (iv) Some squares are circles.In the light of the above statements, choose the most appropriate answer from the options given below.

Only (ii) and (iii) follow.(ii) follows: all circles are triangles, so some triangles must be circles. (iii) follows: all squares are rectangles, so some squares are rectangles.(i) does not follow. All squares are rectangles and no triangle is a rectangle, so no triangle can be a square. (iv) does not follow either: circles are triangles and no triangle is a rectangle, so no circle is a rectangle, and since every square is a rectangle, no square can be a circle.

Q: The question given below has a set of three or four statements. Each set of statements is further divided into three segments. Choose the alternative where the third segment in the statement can be logically deduced using both the preceding two, but not just from one of them. Statement - A. All beggars are poor. All lions are poor. So, all lions are beggars. B. All people are boxes. All foxes are people. So, all boxes are foxes. C. All men can run. All women are men. So, all women can run.

Correct answer: CIn C the middle term is properly distributed: all women are men and all men can run, so all women can run - the third segment does follow from the two before it. In A and B the middle term appears as a predicate in both premises, which proves nothing: two classes both contained in a third need not overlap.

Q: The question given below has a set of three or four statements. Each set of statements is further divided into three segments. Choose the alternative where the third segment in the statement can be logically deduced using both the preceding two, but not just from one of them. Statement - I. Some pens are books. II. All temples are books. III. Some libraries are temples. Conclusion - I. Some libraries are pens. II. Some pens are temples. III. Some libraries are books.

Correct answer: Only III followsSome libraries are temples and all temples are books, so some libraries are books - conclusion III. Conclusions I and II both try to reach pens, and the only statement about pens is a particular one, which cannot carry a conclusion. Only III follows.

Important Instructions

21.

Which of the following statements is/are correct?

1. If all jasmines are flowers and some flowers are white, then some jasmines may be white.
2. If all rats are mammals and all mammals are animal, then all rats are animals.

Select the answer using the codes given below:

A.1 only
B.2 only
C.Both 1 and 2
D.Neither 1 nor 2

Exam Year(s)

Haryana Civil Services - 2026, HPSC - 2026,

Answer: C

Both 1 and 2 are correct.

Statement 1: all jasmines are flowers and some flowers are white. The white flowers may or may not include jasmines, so 'some jasmines may be white' is a possibility that the premises allow. A definite 'some jasmines are white' would not follow, but 'may be' does.

Statement 2 is a valid chain: all rats are mammals and all mammals are animals, so all rats are animals.

So neither statement oversteps its premises, and the answer is both.

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22.

Consider the following pairs:

1. All roses are flowers : Some flowers are roses
2. Some students are athletes : All athletes are students
3. No cats are dogs : No dogs are cats.

How many of the above pairs are correctly matched?

A.Only one pair
B.Only two pairs
C.All three pairs
D.None of the pairs

Exam Year(s)

Haryana Civil Services - 2026, HPSC - 2026,

Answer: B

Only two pairs are correctly matched.

Each pair gives a statement and a conclusion drawn by converting it.

Pair 1: 'All roses are flowers' converts by limitation to 'Some flowers are roses'. Valid.
Pair 2: 'Some students are athletes' converts only to 'Some athletes are students'; it says nothing about all athletes. Invalid.
Pair 3: a universal negative converts simply: 'No cats are dogs' means 'No dogs are cats'. Valid.

So pairs 1 and 3 match and pair 2 does not.

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23.

The question given below contains four arguments of three sentences each. Choose the set in which the third statement is a logical conclusion of the first two.

1. All Ts are square; All squares are rectangular; All Ts are rectangular.
2. Some fat are elongated; Some elongated things are huge; Some fat are huge.
3. Idiots are bumblers; Bumblers fumble; Idiots fumble.
4. Water is good for health; Health foods are rare; Water is rare.

A.4 only
B.3 only
C.Both 1 & 3
D.1, 2, 3 & 4

Exam Year(s)

Haryana Civil Services - 2026, HPSC - 2026,

Answer: C

The valid sets are 1 and 3.

Set 1: all Ts are squares and all squares are rectangular, so all Ts are rectangular. A valid chain.

Set 3: idiots are bumblers and bumblers fumble, so idiots fumble. Also a valid chain.

Set 2 is invalid: the fat things that are elongated need not be among the elongated things that are huge, so two 'some' premises prove nothing. Set 4 is invalid: water is good for health, but that does not make water a 'health food', and even if it were, 'health foods are rare' would not make water rare. So '4 only' and '1, 2, 3 & 4' are wrong, and '3 only' misses set 1.

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24.

Some cricket players are tennis players. All tennis players are hockey players. Which of the following is definitely true ?

A.All cricket players are hockey players.
B.Some cricket players are not hockey players.
C.Some tennis players are not hockey players.
D.Some cricket players are hockey players.

Exam Year(s)

MPPSC State Service - 2024, MPPSC Forest Service - 2024,

Answer: D

The definite conclusion is Some cricket players are hockey players.

Some cricket players are tennis players, and every tennis player is a hockey player. So those cricket players who play tennis are certainly hockey players, which means at least some cricket players are hockey players.

'All cricket players are hockey players' does not follow, because the cricketers who do not play tennis may or may not play hockey. 'Some cricket players are not hockey players' is only possible, not certain. 'Some tennis players are not hockey players' contradicts the second statement.

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25.

If 'No S is P' is a false statement, then which of these statements is necessarily true ?

A.All S is P
B.Some S is P
C.Some S is not P
D.None of the above

Exam Year(s)

MPPSC State Service - 2023, MPPSC Forest Service - 2023,

Answer: B

If 'No S is P' is false, then Some S is P is necessarily true.

In traditional logic, 'No S is P' (a universal negative, E) and 'Some S is P' (a particular affirmative, I) are contradictories: exactly one of them is true. So when 'No S is P' is false, 'Some S is P' must be true.

'All S is P' may or may not be true: it is possible that only some S are P. 'Some S is not P' is also undetermined, since every S might be P. Only 'Some S is P' follows necessarily, so 'None of the above' is wrong too.

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26.

Consider the following argument :

"In order to be a teacher, one must graduate from college. All poets are poor. Some Mathematicians are poets. No college graduate is poor." Which one of the following is not a valid conclusion regarding the above argument ?

A.Some Mathematicians are not teachers.
B.Some teachers are not Mathematicians.
C.Teachers are not poor.
D.Poets are not teachers.

Exam Year(s)

Punjab Civil Service - 2025,

Answer: B

The conclusion that is not valid is Some teachers are not Mathematicians.

From the premises: every teacher is a graduate, no graduate is poor, so no teacher is poor (option c follows). All poets are poor, so no poet is a graduate and hence no poet is a teacher (option d follows). Some mathematicians are poets, and those cannot be teachers, so some mathematicians are not teachers (option a follows).

Nothing in the argument says anything about teachers who are not mathematicians; all teachers might be mathematicians who are not poets. So option (b) does not follow.

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27.

Consider the given statements to be true even if they seem to be at variance from the commonly known facts. Decide which of the conclusions logically follow the given statements.

Statements:
Some computers are machines. Some laptops are computers. All desktops are computers.

Conclusions:
I. Some desktops are machines.
II. Some Laptops are desktops.

Choose the most appropriate answer from below given options:

A.Only Conclusion I follows.
B.Only Conclusion II follows.
C.Both Conclusions I and II follow.
D.Neither Conclusion I nor II follows.

Exam Year(s)

RSMSSB - 2026, RSMSSB Mahila Supervisor - 2026,

Answer: D

The answer is Neither Conclusion I nor II follows.

All desktops are computers, but only some computers are machines. The computers that are machines need not include any desktops, so 'Some desktops are machines' is possible but not certain. Conclusion I does not follow.

Some laptops are computers and all desktops are computers, but two groups both lying inside 'computers' need not overlap. 'Some laptops are desktops' is likewise only a possibility, so Conclusion II does not follow either.

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28.

Which conclusion would follow on the basis of the given statements ?

Statements : (a) All circles are triangles. (b) No triangle is rectangle. (c) All squares are rectangles.

Conclusions : (i) Some triangles are squares. (ii) Some triangles are circles. (iii) Some squares are rectangles. (iv) Some squares are circles.

In the light of the above statements, choose the most appropriate answer from the options given below.

A.Only (i) and (iv) follow
B.Only (i) and (ii) follow
C.Only (ii) and (iii) follow
D.Only (iii) and (iv) follow

Exam Year(s)

RSMSSB - 2024, RSMSSB Mahila Supervisor - 2024,

Answer: C

Only (ii) and (iii) follow.

(ii) follows: all circles are triangles, so some triangles must be circles. (iii) follows: all squares are rectangles, so some squares are rectangles.

(i) does not follow. All squares are rectangles and no triangle is a rectangle, so no triangle can be a square. (iv) does not follow either: circles are triangles and no triangle is a rectangle, so no circle is a rectangle, and since every square is a rectangle, no square can be a circle.

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29.

The question given below has a set of three or four statements. Each set of statements is further divided into three segments. Choose the alternative where the third segment in the statement can be logically deduced using both the preceding two, but not just from one of them.

Statement -

A. All beggars are poor. All lions are poor. So, all lions are beggars.
B. All people are boxes. All foxes are people. So, all boxes are foxes.
C. All men can run. All women are men. So, all women can run.

A.A
B.B
C.C
D.None

Answer: C

Correct answer: C

In C the middle term is properly distributed: all women are men and all men can run, so all women can run - the third segment does follow from the two before it. In A and B the middle term appears as a predicate in both premises, which proves nothing: two classes both contained in a third need not overlap.

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30.

I. Some pens are books.
II. All temples are books.
III. Some libraries are temples.

Conclusion -

I. Some libraries are pens.
II. Some pens are temples.
III. Some libraries are books.

A.Only I follows
B.Only II follows
C.None follows
D.Only III follows

Answer: C

Correct answer: Only III follows

Some libraries are temples and all temples are books, so some libraries are books - conclusion III. Conclusions I and II both try to reach pens, and the only statement about pens is a particular one, which cannot carry a conclusion. Only III follows.

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