Daily Olympiad: Logical Reasoning - Syllogisms [20260511] – 21 Practice Problems & Printable PDF

1. All managers are employees. All employees are workers. Which of the following conclusions necessarily follows?

A. All managers are workers B. All workers are managers C. Some workers are not managers D. No worker is a manager

Solution

Correct: A

From the two universal affirmative premises (All M are E and All E are W), we can chain the relationship: All M are E and All E are W, therefore All M are W. This is a valid syllogism in the first figure (AAA-1). The conclusion 'All managers are workers' follows necessarily. The other options either reverse the relationship or make negative claims not supported by the premises.

2. No poet is a scientist. Some scientists are mathematicians. Which of the following conclusions is valid?

A. Some poets are mathematicians B. No poet is a mathematician C. Some mathematicians are poets D. All mathematicians are scientists

Solution

Correct: B

The middle term 'scientists' is distributed in the first premise (No P are S) but undistributed in the second premise (Some S are M). This is the fallacy of the undistributed middle — the syllogism is invalid. No definite conclusion about poets and mathematicians can be drawn. The correct answer is that no valid conclusion follows, but among the given choices, none is logically entailed. However, if forced, 'No poet is a mathematician' does not necessarily follow because some scientists who are mathematicians might not overlap with poets at all. The syllogism as structured is invalid.

3. Some books are novels. All novels are fiction. Which of the following conclusions necessarily follows?

A. All fiction is novels B. Some books are fiction C. No book is fiction D. All books are novels

Solution

Correct: B

From 'Some B are N' and 'All N are F', we can conclude 'Some B are F' by the chain rule of syllogistic reasoning. Since some books are novels and all novels are fiction, those same books are also fiction. This is a valid conclusion. 'All fiction is novels' reverses the universal premise and is invalid. 'No book is fiction' contradicts the chain. 'All books are novels' overgeneralizes from a particular premise.

4. In a standard-form categorical syllogism, which of the following rules must be satisfied for the syllogism to be valid?

A. The middle term must be distributed in at least one premise B. The middle term must be distributed in both premises C. The major and minor terms must be distributed in the conclusion D. At least one premise must be negative

Solution

Correct: A

The fundamental rule of categorical syllogisms is that the middle term must be distributed at least once. If the middle term is not distributed in either premise, the fallacy of the undistributed middle occurs and the syllogism is invalid. The middle term need not be distributed in both premises. Distribution of the major and minor terms in the conclusion is not always required — only the middle term distribution rule is mandatory for validity.

5. All dogs are animals. Some animals are pets. Which of the following conclusions necessarily follows?

A. Some dogs are pets B. All pets are dogs C. Some animals are not dogs D. No pet is a dog

Solution

Correct: C

The middle term 'animals' is distributed in the first premise (All D are A) but undistributed in the second premise (Some A are P). This is the fallacy of the undistributed middle. We cannot draw any definite conclusion linking dogs and pets. 'Some dogs are pets' is not guaranteed. 'All pets are dogs' and 'No pet is a dog' are also unsupported. The syllogism is invalid as structured.

6. No king is a slave. Some slaves are workers. Which conclusion follows?

A. Some kings are workers B. No king is a worker C. Some workers are kings D. All workers are slaves

Solution

Correct: B

The middle term 'slaves' is distributed in the first premise (No K are S) but undistributed in the second premise (Some S are W). This is again the fallacy of the undistributed middle. No valid conclusion linking kings and workers can be drawn. None of the given options follows necessarily. The syllogism is invalid.

7. All roses are flowers. Some flowers are red. Which of the following is a valid conclusion?

A. All roses are red B. Some roses are red C. No rose is red D. Some red things are roses

Solution

Correct: B

The middle term 'flowers' is distributed in the first premise (All R are F) but undistributed in the second premise (Some F are R). This commits the fallacy of the undistributed middle. We cannot conclude anything definite about roses and redness. 'Some roses are red' is not guaranteed because the red flowers may not be roses. The syllogism is invalid.

8. Some students are athletes. All athletes are healthy. Which conclusion necessarily follows?

A. All healthy people are students B. Some students are healthy C. No student is healthy D. All students are athletes

Solution

Correct: B

From 'Some S are A' and 'All A are H', we can conclude 'Some S are H' by the chain rule. The particular affirmative premise ensures that at least some students share the property of being athletes, and since all athletes are healthy, those students are also healthy. This is a valid syllogism (DAR-3 in figure 3). The other options either reverse the relationship or make unsupported negative claims.

9. No doctor is a quack. Some quacks are consultants. Which of the following conclusions is valid?

A. Some consultants are doctors B. No consultant is a doctor C. Some doctors are consultants D. All consultants are quacks

Solution

Correct: B

The middle term 'quacks' is distributed in the first premise (No D are Q) but undistributed in the second premise (Some Q are C). This is the fallacy of the undistributed middle. No valid conclusion linking doctors and consultants can be drawn. The syllogism is invalid. None of the given conclusions follows necessarily.

10. All A are B. No B are C. What can be concluded about A and C?

A. Some A are C B. No A is C C. All A are C D. Some C are A

Solution

Correct: B

From 'All A are B' and 'No B are C', we can chain the relationship: All A are B and No B are C implies that no member of A can be a member of C, because all A are within B and B shares no members with C. Therefore, 'No A is C' follows validly. This is an E conclusion derived from an A and an E premise, which is valid in the first figure (AEE-1).

11. Some politicians are honest. All honest people are truthful. Which of the following conclusions necessarily follows?

A. All truthful people are politicians B. Some politicians are truthful C. No politician is truthful D. All politicians are honest

Solution

Correct: B

From 'Some P are H' and 'All H are T', we can conclude 'Some P are T' by the chain rule. Since some politicians are honest and all honest people are truthful, those same politicians are also truthful. This is a valid conclusion (DAR-1 in figure 1). The other options either reverse the universal premise or make unsupported claims.

12. All managers are employees. Some employees are skilled. Which conclusion is valid?

A. All managers are skilled B. Some managers are skilled C. No manager is skilled D. Some skilled people are managers

Solution

Correct: B

The middle term 'employees' is distributed in the first premise (All M are E) but undistributed in the second premise (Some E are S). This is the fallacy of the undistributed middle. We cannot conclude anything definite about managers and skilled people. 'Some managers are skilled' is not guaranteed because the skilled employees may not include any managers. The syllogism is invalid.

13. Some fruits are sweet. No sweet thing is sour. Which conclusion follows?

A. All sweet things are fruits B. Some fruits are not sour C. No fruit is sweet D. All sour things are fruits

Solution

Correct: B

From 'Some F are S' and 'No S are O' (where O = sour), we can conclude 'Some F are not O' — that is, some fruits are not sour. This follows because the particular fruits that are sweet cannot be sour (since no sweet thing is sour). The conclusion 'Some fruits are not sour' is valid. The other options either reverse relationships or contradict the premises.

14. All poets are sensitive. Some sensitive people are artists. Which conclusion is valid?

A. All artists are poets B. Some poets are artists C. No poet is an artist D. All sensitive people are poets

Solution

Correct: B

The middle term 'sensitive people' is distributed in the first premise (All P are S) but undistributed in the second premise (Some S are A). This is the fallacy of the undistributed middle. We cannot conclude that some poets are artists because the artists who are sensitive may not overlap with poets. The syllogism is invalid. None of the given conclusions follows necessarily.

15. No bird is a mammal. All mammals are warm-blooded. What necessarily follows?

A. Some birds are warm-blooded B. No bird is warm-blooded C. All warm-blooded animals are mammals D. Some warm-blooded animals are birds

Solution

Correct: B

From 'No B are M' and 'All M are W', we cannot conclude anything definite about birds and warm-bloodedness. The middle term 'mammals' is distributed in the first premise (No B are M) but the conclusion about B and W is not entailed. Birds might or might not be warm-blooded — the premises do not address this. The syllogism does not yield a valid conclusion about birds and warm-blooded animals.

16. Some students passed. All who passed are eligible. Which conclusion necessarily follows?

A. All eligible people are students B. Some students are eligible C. No student is eligible D. All students passed

Solution

Correct: B

From 'Some S are P' and 'All P are E', we can conclude 'Some S are E' by the chain rule. Since some students passed and all who passed are eligible, those students are also eligible. This is a valid syllogistic conclusion. The other options either reverse the relationship or make unsupported negative claims.

17. All triangles are polygons. Some polygons are regular. Which conclusion is valid?

A. All triangles are regular B. Some triangles are regular C. No triangle is regular D. All regular shapes are triangles

Solution

Correct: B

The middle term 'polygons' is distributed in the first premise (All T are P) but undistributed in the second premise (Some P are R). This is the fallacy of the undistributed middle. We cannot conclude anything definite about triangles and regularity. The regular polygons may or may not include triangles. The syllogism is invalid.

18. No criminal is innocent. Some suspects are innocent. What conclusion follows?

A. Some suspects are criminals B. No suspect is a criminal C. Some criminals are suspects D. All suspects are innocent

Solution

Correct: B

From 'No C are I' and 'Some S are I', we can use the process of elimination. Since no criminal is innocent and some suspects are innocent, those innocent suspects cannot be criminals. However, this does not directly give a conclusion about suspects and criminals. The valid conclusion is that some suspects are not criminals, but that option is not listed. Among the given choices, none follows necessarily. The syllogism does not yield a valid conclusion linking suspects and criminals.

19. Some scientists are curious. All curious people are open-minded. Which conclusion necessarily follows?

A. All open-minded people are scientists B. Some scientists are open-minded C. No scientist is open-minded D. All curious people are scientists

Solution

Correct: B

From 'Some S are C' and 'All C are O', we can conclude 'Some S are O' by the chain rule. Since some scientists are curious and all curious people are open-minded, those scientists are also open-minded. This is a valid conclusion. The other options either reverse the universal premise or make unsupported negative claims.

20. All fathers are males. No male is a female. What conclusion follows about fathers and females?

A. Some fathers are females B. All fathers are females C. No father is a female D. Some females are fathers

Solution

Correct: C

From 'All F are M' and 'No M are Fm' (where Fm = female), we can chain the relationship. All fathers are males, and no male is a female, so no father can be a female. Therefore, 'No father is a female' follows validly. This is an E conclusion derived from an A and an E premise (AEE-1), which is a valid mood in the first figure.

21. Some employees are punctual. All punctual people are disciplined. Which conclusion is valid?

A. All disciplined people are employees B. Some employees are disciplined C. No employee is disciplined D. All punctual people are employees

Solution

Correct: B

From 'Some E are P' and 'All P are D', we can conclude 'Some E are D' by the chain rule. Since some employees are punctual and all punctual people are disciplined, those employees are also disciplined. This is a valid syllogistic conclusion. The other options either reverse the universal premise or make unsupported negative claims.

Daily Olympiad: Logical Reasoning - Syllogisms [20260511]

1. All managers are employees. All employees are workers. Which of the following conclusions necessarily follows?

2. No poet is a scientist. Some scientists are mathematicians. Which of the following conclusions is valid?

3. Some books are novels. All novels are fiction. Which of the following conclusions necessarily follows?

4. In a standard-form categorical syllogism, which of the following rules must be satisfied for the syllogism to be valid?

5. All dogs are animals. Some animals are pets. Which of the following conclusions necessarily follows?

6. No king is a slave. Some slaves are workers. Which conclusion follows?

7. All roses are flowers. Some flowers are red. Which of the following is a valid conclusion?

8. Some students are athletes. All athletes are healthy. Which conclusion necessarily follows?

9. No doctor is a quack. Some quacks are consultants. Which of the following conclusions is valid?

10. All A are B. No B are C. What can be concluded about A and C?

11. Some politicians are honest. All honest people are truthful. Which of the following conclusions necessarily follows?

12. All managers are employees. Some employees are skilled. Which conclusion is valid?

13. Some fruits are sweet. No sweet thing is sour. Which conclusion follows?

14. All poets are sensitive. Some sensitive people are artists. Which conclusion is valid?

15. No bird is a mammal. All mammals are warm-blooded. What necessarily follows?

16. Some students passed. All who passed are eligible. Which conclusion necessarily follows?

17. All triangles are polygons. Some polygons are regular. Which conclusion is valid?

18. No criminal is innocent. Some suspects are innocent. What conclusion follows?

19. Some scientists are curious. All curious people are open-minded. Which conclusion necessarily follows?

20. All fathers are males. No male is a female. What conclusion follows about fathers and females?

21. Some employees are punctual. All punctual people are disciplined. Which conclusion is valid?

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