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 door is a window. No rack is a door. All cupboards are windows. Conclusions: I. Some cupboards are racks. II. No cupboard is a door. III. No rack is a window.
Only conclusion II follows
Understanding Statements and Conclusions in Logic
This question asks us to evaluate which conclusions logically follow from a set of given statements, assuming the statements are true regardless of real-world facts. This type of problem is common in logical reasoning tests and relies on deductive logic.
Analyzing the Given Statements
Let's break down the provided statements:
- Statement 1: No door is a window. This establishes a relationship of mutual exclusion between 'door' and 'window'. If something is a door, it cannot be a window, and vice versa.
- Statement 2: No rack is a door. This establishes a relationship of mutual exclusion between 'rack' and 'door'. If something is a rack, it cannot be a door, and vice versa.
- Statement 3: All cupboards are windows. This establishes a hierarchical relationship. The set of 'cupboards' is a subset of the set of 'windows'. If something is a cupboard, it must also be a window.
Visualizing Relationships (Conceptual)
We can think of these relationships using diagrams. Imagine circles representing categories. The statements tell us:
- The 'Door' circle and the 'Window' circle do not overlap.
- The 'Rack' circle and the 'Door' circle do not overlap.
- The 'Cupboard' circle is entirely contained within the 'Window' circle.
Note that the relationship between 'Rack' and 'Window' or 'Rack' and 'Cupboard' is not directly specified by the statements. Racks are not doors, and doors are not windows. This doesn't automatically mean racks cannot be windows or cupboards.
Evaluating the Conclusions
Now, let's assess each conclusion based on the statements.
Conclusion I: Some cupboards are racks.
From Statement 3, we know all cupboards are windows. From Statement 2, we know no racks are doors. There is no statement directly linking 'cupboards' (or 'windows') to 'racks'. Just because racks are not doors, and doors are not windows, doesn't mean racks must overlap with windows (where cupboards are located). We cannot logically deduce any relationship (overlap or no overlap) between cupboards and racks from the given information.
Therefore, Conclusion I does not follow.
Conclusion II: No cupboard is a door.
Let's use the statements to check this. Statement 3: All cupboards are windows. Statement 1: No door is a window (which also means No window is a door). If something is a cupboard, then according to Statement 3, it must be a window. If it is a window, then according to Statement 1, it cannot be a door. So, if something is a cupboard, it cannot be a door.
This conclusion logically follows from the given statements.
Conclusion III: No rack is a window.
From Statement 2, we know no rack is a door. From Statement 1, we know no door is a window. These statements establish that Racks are not Doors, and Doors are not Windows. However, they do not provide any information about the relationship between Racks and Windows. Racks could potentially be windows, or they could be something else entirely (neither doors nor windows). The statements do not exclude the possibility of a rack being a window.
Therefore, Conclusion III does not follow.
Summary of Conclusions
Based on our analysis:
- Conclusion I: Some cupboards are racks. (Does NOT follow)
- Conclusion II: No cupboard is a door. (Follows)
- Conclusion III: No rack is a window. (Does NOT follow)
Only Conclusion II logically follows from the given statements.
| Conclusion | Analysis | Logically Follows? |
|---|---|---|
| I. Some cupboards are racks. | No direct link between Cupboards/Windows and Racks established. | No |
| II. No cupboard is a door. | All cupboards are windows; No window is a door. Therefore, No cupboard is a door. | Yes |
| III. No rack is a window. | No direct link between Racks and Windows established. Racks could be windows. | No |
Revision Table: Key Relationships
| Category 1 | Relationship | Category 2 | Based on Statement |
|---|---|---|---|
| Door | Mutually exclusive | Window | Statement 1 |
| Rack | Mutually exclusive | Door | Statement 2 |
| Cupboard | Subset of | Window | Statement 3 |
Additional Information: Deductive vs Inductive Logic
This problem uses deductive logic. Deductive logic starts with general statements (premises) and draws conclusions that must be true if the premises are true. If the premises are true, the conclusion is guaranteed to be true. This is different from inductive logic, which uses specific observations to arrive at general conclusions that are probable but not guaranteed.
In solving statement and conclusion problems:
- Always assume the statements are absolutely true, even if they contradict common knowledge.
- Only draw conclusions that are strictly and necessarily derived from the given statements.
- Do not use outside information or assumptions about the real world.
The goal is to test your ability to follow logical rules based purely on the provided information.
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:
All dancers are talented.
Some girls are dancers.
Conclusions:
I. Some girls are talented.
II. All talented are girls.
III. All girls are talented.
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 directors are actors.
No actor is a producer.
All choreographers are directors.
Conclusions:
I. No choreographer is producer.
II. Some actors are choreographers.
III. No director is a producer.
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 follows from the statements.
Statements:
All lemons are plums.
All plums are dates.
Some dates are mangoes.
Conclusions:
I. Some lemons are mangoes.
II. Some mangoes are plums.
III. All lemons are dates.
IV. Some mangoes are dates.
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 cards are postcards.
Some cards are envelopes.
All envelopes are copies.
Conclusions:
I. Some copies are envelopes.
II. Some postcards are copies.
III. Some cards are copies.
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 employees are tax-payers.
Some employees are farmers.
Some farmers are doctors.
Conclusions:
I. No farmer is a tax-payer.
II. Some farmers are tax-payers.
