Syllogism

Syllogism is a form of deductive reasoning where a conclusion is drawn from two or more premises that are asserted or assumed to be true. It is widely used in logical reasoning tests, competitive exams, and to improve critical thinking skills.

Understanding Syllogism

In syllogisms, statements are given which contain three terms — a major term, a minor term, and a middle term. These terms are used to form premises, and based on these premises, conclusions are tested for validity.

Types of Statements / Premises:

Universal Affirmative: All A are B.
Universal Negative: No A is B.
Particular Affirmative: Some A are B.
Particular Negative: Some A are not B.

Terminology:

Major term: The predicate of the conclusion.
Minor term: The subject of the conclusion.
Middle term: Appears in both premises but not in the conclusion.

How to Solve Syllogism Questions?

Read carefully: Understand the premises and identify the three terms.
Analyze relations: Determine relationships between terms (All, Some, None).
Use Venn diagrams or logical reasoning: Visualize sets and their intersections.
Check conclusions: Decide whether each conclusion logically follows from premises.
Answer accordingly: Usually options are:
- Only conclusion I follows
- Only conclusion II follows
- Both conclusions follow
- Neither conclusion follows

20 Practice Questions with Stepwise Solutions

Premises:
1) All cats are animals.
2) Some animals are dogs.
Conclusions:
I. Some cats are dogs.
II. Some animals are cats.
Solution:
1. Identify terms: Cats (A), Animals (B), Dogs (C).
2. Premise 1: All A are B.
3. Premise 2: Some B are C.
4. Conclusion I: Some A are C — Not necessarily true (cats and dogs might be different groups).
5. Conclusion II: Some B are A — True (all cats are animals, so some animals are cats).
6. Answer: Only conclusion II follows.
Premises:
1) No birds are mammals.
2) All crows are birds.
Conclusions:
I. No crows are mammals.
II. Some birds are not crows.
Solution:
1. Terms: Birds (A), Mammals (B), Crows (C).
2. Premise 1: No A is B.
3. Premise 2: All C are A.
4. Conclusion I: No C is B — True.
5. Conclusion II: Some A are not C — Cannot be determined (could all birds be crows?).
6. Answer: Only conclusion I follows.
Premises:
1) All flowers are plants.
2) Some plants are trees.
Conclusions:
I. Some flowers are trees.
II. Some plants are flowers.
Solution:
1. Terms: Flowers (A), Plants (B), Trees (C).
2. Premise 1: All A are B.
3. Premise 2: Some B are C.
4. Conclusion I: Some A are C — Cannot be determined.
5. Conclusion II: Some B are A — True (since all flowers are plants, some plants are flowers).
6. Answer: Only conclusion II follows.
Premises:
1) Some books are magazines.
2) All magazines are journals.
Conclusions:
I. Some journals are books.
II. Some books are journals.
Solution:
1. Terms: Books (A), Magazines (B), Journals (C).
2. Premise 1: Some A are B.
3. Premise 2: All B are C.
4. Conclusion I: Some C are A — Cannot be determined.
5. Conclusion II: Some A are C — True.
6. Answer: Only conclusion II follows.
Premises:
1) All doctors are professionals.
2) No professional is lazy.
Conclusions:
I. No doctor is lazy.
II. Some professionals are doctors.
Solution:
1. Terms: Doctors (A), Professionals (B), Lazy (C).
2. Premise 1: All A are B.
3. Premise 2: No B is C.
4. Conclusion I: No A is C — True.
5. Conclusion II: Some B are A — True.
6. Answer: Both conclusions I and II follow.
Premises:
1) Some fruits are sweet.
2) All sweet things are healthy.
Conclusions:
I. Some fruits are healthy.
II. All healthy things are sweet.
Solution:
1. Terms: Fruits (A), Sweet (B), Healthy (C).
2. Premise 1: Some A are B.
3. Premise 2: All B are C.
4. Conclusion I: Some A are C — True.
5. Conclusion II: All C are B — Cannot be determined.
6. Answer: Only conclusion I follows.
Premises:
1) No pen is pencil.
2) Some pencils are erasers.
Conclusions:
I. Some erasers are not pens.
II. No eraser is pen.
Solution:
1. Terms: Pen (A), Pencil (B), Eraser (C).
2. Premise 1: No A is B.
3. Premise 2: Some B are C.
4. Conclusion I: Some C are not A — True.
5. Conclusion II: No C is A — Cannot be determined.
6. Answer: Only conclusion I follows.
Premises:
1) All rivers are water bodies.
2) Some water bodies are lakes.
Conclusions:
I. Some rivers are lakes.
II. Some water bodies are rivers.
Solution:
1. Terms: Rivers (A), Water bodies (B), Lakes (C).
2. Premise 1: All A are B.
3. Premise 2: Some B are C.
4. Conclusion I: Some A are C — Cannot be determined.
5. Conclusion II: Some B are A — True.
6. Answer: Only conclusion II follows.
Premises:
1) Some cars are bikes.
2) No bike is a truck.
Conclusions:
I. Some trucks are cars.
II. Some cars are not trucks.
Solution:
1. Terms: Cars (A), Bikes (B), Trucks (C).
2. Premise 1: Some A are B.
3. Premise 2: No B is C.
4. Conclusion I: Some C are A — Cannot be determined.
5. Conclusion II: Some A are not C — True.
6. Answer: Only conclusion II follows.
Premises:
1) All trees are plants.
2) All plants are living things.
Conclusions:
I. All trees are living things.
II. Some living things are trees.
Solution:
1. Terms: Trees (A), Plants (B), Living things (C).
2. Premise 1: All A are B.
3. Premise 2: All B are C.
4. Conclusion I: All A are C — True.
5. Conclusion II: Some C are A — True.
6. Answer: Both conclusions I and II follow.
Premises:
1) Some teachers are players.
2) All players are athletes.
Conclusions:
I. Some teachers are athletes.
II. All athletes are teachers.
Solution:
1. Terms: Teachers (A), Players (B), Athletes (C).
2. Premise 1: Some A are B.
3. Premise 2: All B are C.
4. Conclusion I: Some A are C — True.
5. Conclusion II: All C are A — Cannot be determined.
6. Answer: Only conclusion I follows.
Premises:
1) No pen is a book.
2) All books are paper.
Conclusions:
I. No paper is a pen.
II. Some paper are books.
Solution:
1. Terms: Pen (A), Book (B), Paper (C).
2. Premise 1: No A is B.
3. Premise 2: All B are C.
4. Conclusion I: No C is A — Cannot be determined.
5. Conclusion II: Some C are B — True.
6. Answer: Only conclusion II follows.
Premises:
1) Some dogs are pets.
2) Some pets are cats.
Conclusions:
I. Some dogs are cats.
II. Some cats are pets.
Solution:
1. Terms: Dogs (A), Pets (B), Cats (C).
2. Premise 1: Some A are B.
3. Premise 2: Some B are C.
4. Conclusion I: Some A are C — Cannot be determined.
5. Conclusion II: Some C are B — True.
6. Answer: Only conclusion II follows.
Premises:
1) All boys are students.
2) No student is lazy.
Conclusions:
I. No boy is lazy.
II. Some students are boys.
Solution:
1. Terms: Boys (A), Students (B), Lazy (C).
2. Premise 1: All A are B.
3. Premise 2: No B is C.
4. Conclusion I: No A is C — True.
5. Conclusion II: Some B are A — True.
6. Answer: Both conclusions I and II follow.
Premises:
1) Some cars are red.
2) Some red things are expensive.
Conclusions:
I. Some cars are expensive.
II. Some expensive things are red.
Solution:
1. Terms: Cars (A), Red things (B), Expensive things (C).
2. Premise 1: Some A are B.
3. Premise 2: Some B are C.
4. Conclusion I: Some A are C — Cannot be determined.
5. Conclusion II: Some C are B — True.
6. Answer: Only conclusion II follows.
Premises:
1) All teachers are educated.
2) Some educated are strict.
Conclusions:
I. Some teachers are strict.
II. Some strict are educated.
Solution:
1. Terms: Teachers (A), Educated (B), Strict (C).
2. Premise 1: All A are B.
3. Premise 2: Some B are C.
4. Conclusion I: Some A are C — Cannot be determined.
5. Conclusion II: Some C are B — True.
6. Answer: Only conclusion II follows.
Premises:
1) No apples are oranges.
2) All apples are fruits.
Conclusions:
I. No orange is fruit.
II. Some fruits are apples.
Solution:
1. Terms: Apples (A), Oranges (B), Fruits (C).
2. Premise 1: No A is B.
3. Premise 2: All A are C.
4. Conclusion I: No B is C — Cannot be determined.
5. Conclusion II: Some C are A — True.
6. Answer: Only conclusion II follows.
Premises:
1) Some students are intelligent.
2) All intelligent people are successful.
Conclusions:
I. Some students are successful.
II. All successful people are intelligent.
Solution:
1. Terms: Students (A), Intelligent (B), Successful (C).
2. Premise 1: Some A are B.
3. Premise 2: All B are C.
4. Conclusion I: Some A are C — True.
5. Conclusion II: All C are B — Cannot be determined.
6. Answer: Only conclusion I follows.
Premises:
1) All fruits are edible.
2) Some edible things are sweet.
Conclusions:
I. Some fruits are sweet.
II. Some sweet things are edible.
Solution:
1. Terms: Fruits (A), Edible (B), Sweet (C).
2. Premise 1: All A are B.
3. Premise 2: Some B are C.
4. Conclusion I: Some A are C — Cannot be determined.
5. Conclusion II: Some C are B — True.
6. Answer: Only conclusion II follows.
Premises:
1) Some cars are electric.
2) No electric things are petrol powered.
Conclusions:
I. Some cars are not petrol powered.
II. No petrol powered thing is electric.
Solution:
1. Terms: Cars (A), Electric (B), Petrol powered (C).
2. Premise 1: Some A are B.
3. Premise 2: No B is C.
4. Conclusion I: Some A are not C — True.
5. Conclusion II: No C is B — True.
6. Answer: Both conclusions I and II follow.

Summary

Syllogism questions test your ability to logically deduce conclusions from given premises using concepts of set theory and relations. Practice visualizing these premises with Venn diagrams or mental logic, and always carefully analyze each conclusion to decide if it necessarily follows.

With continuous practice, you will develop accuracy and speed in solving these questions in competitive exams.