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: 1. No bed is a chair. 2. All tables are beds. 3. No cupboard is a bed. Conclusions: I. No table is a chair. II. No cupboard is a table. III. Some beds are tables.
Syllogism Question Analysis
This question involves analyzing three statements and determining which of the given conclusions logically follow from these statements. We must assume the statements are true, regardless of whether they align with real-world knowledge.
Analyzing the Statements
Let's break down the provided statements:
- Statement 1: No bed is a chair. This indicates there is no overlap between the set of beds and the set of chairs. They are mutually exclusive.
- Statement 2: All tables are beds. This means the set of tables is entirely contained within the set of beds. Tables are a subset of beds.
- Statement 3: No cupboard is a bed. This indicates there is no overlap between the set of cupboards and the set of beds. They are mutually exclusive.
Analyzing the Conclusions
Now, let's evaluate each conclusion based on the statements:
- Conclusion I: No table is a chair.
- Conclusion II: No cupboard is a table.
- Conclusion III: Some beds are tables.
Evaluating Each Conclusion Logically
We will check if each conclusion can be derived from the given statements.
Evaluation of Conclusion I: No table is a chair
From Statement 2, we know "All tables are beds". This means if something is a table, it must also be a bed.
From Statement 1, we know "No bed is a chair". This means if something is a bed, it cannot be a chair.
Combining these: If all tables are beds, and no bed can be a chair, then it logically follows that no table can be a chair. If a table were a chair, it would have to be a bed (from statement 2) and also a chair (as assumed), but statement 1 says no bed is a chair, creating a contradiction. Thus, this conclusion is true.
Evaluation of Conclusion II: No cupboard is a table
From Statement 3, we know "No cupboard is a bed". This means if something is a cupboard, it cannot be a bed.
From Statement 2, we know "All tables are beds". This means if something is a table, it must be a bed.
Combining these: If no cupboard is a bed, and all tables are beds, then a cupboard cannot be a table. If a cupboard were a table, it would have to be a bed (from statement 2), but statement 3 says no cupboard is a bed, a contradiction. Thus, this conclusion is true.
Evaluation of Conclusion III: Some beds are tables
From Statement 2, we know "All tables are beds". This statement implies that the set of tables is contained within the set of beds. If the set of tables is not empty (which is usually assumed in such problems unless stated otherwise), then there are tables, and since all of them are beds, there must be some beds that are tables. This is a direct implication of "All A are B" meaning "Some B are A" (provided A is not empty). Thus, this conclusion is true.
Summary of Conclusions
Let's summarize our findings:
- Conclusion I: No table is a chair - Follows
- Conclusion II: No cupboard is a table - Follows
- Conclusion III: Some beds are tables - Follows
Since all three conclusions logically follow from the given statements, the correct option is the one stating that all conclusions follow.
| Conclusion | Statements Used | Logic | Follows? |
|---|---|---|---|
| I. No table is a chair. | Statements 1 & 2 | All Tables <span>→</span> Beds, No Bed <span>→</span> Chair. Therefore, No Table <span>→</span> Chair. | Yes |
| II. No cupboard is a table. | Statements 2 & 3 | No Cupboard <span>→</span> Bed, All Tables <span>→</span> Beds. Therefore, No Cupboard <span>→</span> Table. | Yes |
| III. Some beds are tables. | Statement 2 | All Tables <span>→</span> Beds directly implies Some Beds <span>→</span> Tables. | Yes |
Final Answer
Based on our analysis, all three conclusions (I, II, and III) logically follow from the given statements.
Revision Table: Syllogism Concepts
| Statement Type | Relation | Example (All A are B) | Converse |
|---|---|---|---|
| All A are B | A is a subset of B | All dogs are mammals. | Some B are A (if A exists) |
| No A is B | A and B are disjoint | No cat is a dog. | No B is A |
| Some A are B | A and B intersect | Some students are engineers. | Some B are A |
| Some A are not B | Part of A is outside B | Some students are not engineers. | Does not necessarily follow |
Additional Information: Solving Syllogism Problems
Syllogism questions test your ability to deduce conclusions from given premises. Here are some tips for solving them:
- Assume Statements are True: Always treat the statements as absolutely true, even if they contradict common knowledge.
- Use Venn Diagrams: Visualizing the relationships between categories using Venn diagrams can be very helpful. Draw circles representing the sets (Beds, Chairs, Tables, Cupboards) and show the overlap or separation based on the statements.
- Analyze Each Conclusion Separately: Test each conclusion against the combined information from the statements.
- Look for Negative Inferences: Pay attention to "No" statements as they establish separation between categories.
- Understand Conversions: Learn how statements can be converted (e.g., "All A are B" implies "Some B are A").
- Practice: Solving various types of syllogism problems will improve your speed and accuracy.
Similar Questions
- All flowers are plants. Some plants are flowering plants. Which conclusion is logically valid?
Two 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 f act s, decide which of the conclusions logically follow(s) from the statements.
Statements:
Some carpenters are singers.
All singers are doctors.
Conclusions:
I. No doctor is a carpenter.
II. Some doctors are singers.
III. Some carpenters are doctors.
Three statements are given, followed by three conclusions numbered I, II and III. Assuming the statement s 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 machines are coolers.
All coolers are robots.
Some microwaves are coolers.
Conclusions:
I. Some coolers are machines.
II. Some robots are machines.
III. No robot is a microwave.
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:
1. All teachers are students.
2. All principal are teachers.
3. Some principals are doctors.
Conclusions:
I. Some students are teachers.
II. No student is a doctor.
III. Some students are principals.Two 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:
1. All apples are mangoes.
2. Some bananas are mangoes.
Conclusions:
I. Some mangoes are bananas.
II. Some mangoes are apples.
III. No mango is an apple.Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
1. No city is a district.
2. Some districts are zones.
3. Some zones are states.
Conclusions:
I. Some zones are districts.
II. Some districts are cities.
lII. No state is a zone.
Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
1. Some tables are chairs.
2. Some chairs are beds.
3. All beds are goods.
Conclusions:
I. Some chairs are goods.
Il. Some goods are not beds.
Read the given statements and conclusions carefully. Assuming that the information given in the statements is ture, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
No man is engineer.
No engineer is driver.
Some drivers are shop-keepers.
Conclusions:
1. Some men are drivers.
2. No shop-keepers are engineer.
3. Some shop-keepers are not engineers.
Read the given statements and conclusions carefully. Assuming that the information given in the statements is ture, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
All aero-planes are cars.
All helicopters are cars.
All cars are scooters.
Conclusions:
1. All helicopters are scooters.
2. Some aero-planes are helicopters.
3. No aero-plane is helicopter.
Read the given statements and conclusions carefully. Assuming that the information given in the statement is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
Some pillows are doors.
Some doors are beds.
Conclusions:
I. Some doors are pillows.
II. All beds are doors.
Important Questions from Syllogism
Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
Some students are players.
All players are male.
Conclusions:
I. All males are players.
II. Some males are students.
Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
No creative is an employer.
All experts are creative.
All workers are experts.
Conclusions:
I. No employer is an expert.
II. No worker is an employer.
Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
Some actors are choreographers.
All choreographers are producers.
Not a single producer is a director.
Conclusions:
I. Some actors are directors.
II. Not a single actor is a director.
Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements :
1. All flowers are tulips.
2. No tulips are whites.
Conclusions :
I. All tulips are flowers.
II. Some tulips are whites.
Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
All rats are dogs.
Some rats are hens.
Conclusions:
I. Some rats are dogs.
II. Some hens are rats.
