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.
Similar Questions
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.
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:
Some spices are medicines.
All medicines are chemicals.
No chemical is cheap.
Conclusions:
I. Some medicines are cheap.
II. Some chemicals are spices.
III. No medicine is cheap.
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:
All oranges are apples.
Some oranges are bananas.
All bananas are fruits.
Conclusions:
I. Some fruits are apples.
II. Some apples are bananas.
III. Some oranges are fruits.
In the following question below are given some statements followed by some conclusions based on those statements. Taking the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusion logically follows the given statements.
Statements:
I. Some Z are X.
II. Some W are Z.
Conclusions:
I. Some X are not W.
II. Some X are not Z.
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:
Some mobiles are flat.
All flats are TVs.
Some TVs are plastic.
Conclusions:
I. Some mobiles are TVs.
II. Some flats are plastic.
III. All plastic are TVs.
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:
No cup is a plate.
All cups are utensils.
Some bottles are cups.
Conclusions:
I. Some utensils are not plates.
II. Some bottles are not plates.
III. No bottle is a plate.
Three statements are followed by three conclusions numbered I, II and III. You have to consider these statements to be true, even if they seem to be at variance with commonly known facts. Decide which of the given conclusions logically follow/s from the given statements.
Statements:
Some watches are projectors.
All projectors are lamps.
Some heaters are watches.
Conclusions:
(I) Some heaters are projectors.
(II) Some lamps are heaters.
(III) All watches are lamps
In the following question below are given some statements followed by some conclusions based on those statements. Taking the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusion logically follows the given statements.
Statements:
I. No A is B.
II. No C is B.
Conclusion:
I. Some C are not A.
II. Some A are B.
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 benches are tables.
Some tables are chairs.
Some chairs are pencils.
Conclusions:
I. Some benches are chairs.
II. Some tables are pencils.
III. Some pencils are chairs.
IV. Some pencils are tables.
Important Questions from Syllogism
The statements below are followed by conclusions labeled I, II and III. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.
Statements:
All twenty are thirty.
All thirty are forty.
All forty are sixty.
All sixty are seventy.
Conclusions:
I. Some forty are thirty.
II. Some seventy are sixty.
III. No thirty is twenty.The statements below are followed by two conclusions labelled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.
Statements:
All Strong are animals.
Some animals are Tigers.
All Tigers are Sharp.
Conclusions:
I. Some Strong are Sharp.
II. No Strong is Sharp.The statements below are followed by conclusions labelled I, II and III. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.Statements:
Some women are weak.
Some weaks are female.
All female are iron.
All iron are gold.Conclusions:
I. Some weaks are iron.
II. Some gold are weaks.
III. Some women are female.
The statements below are followed by two conclusions labeled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.Statements:
Some teaspoons are glasses.
All teddies are teaspoons.
Conclusions:
I. Some teddies are glasses.
II. Some glasses are teddies.
The statements below are followed by two conclusions labeled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally Established facts, decide which conclusion(s) logically and definitely follow(s) from the Information, Given in the Statements.
Statements:
All bangles are rings.
Some rings are toys.
Some toys are dolls.
Conclusions:
I. Some rings are bangles.
II. Some dolls are rings.
