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 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.
Consider the given statement(s) to be true and decide which of the given conclusions/assumptions can definitely be drawn from the given statement.
Statement 1: All elephants are men.
Statement 2: All men are socks.
Conclusion I: Some socks are elephants.
Conclusion II: All elephants are socks.In the question, a word is represented by only one set of numbers as given in any one of the alternatives. The sets of numbers given in the question are represented by two classes of alphabets in two matrices given below. The columns and rows of Matrix 1 are numbered from 0 to 4 and that of Matrix II are numbered from 5 to 9. A letter from these matrices can be represented first by its row and next by its column, e.g., 'A' can be represented by 04, 12, etc., and 'U' can be represented by 59, 66, etc. Similarly, you have to identify the set for the word 'ROOT'.
MATRIX I
0 1 2 3 4 0 B C D E A 1 D E A B C 2 C D E A B 3 A B C D E 4 E A B C D MATRIX II
5 6 7 8 9 5 R O N T U 6 T U R O N 7 O N T U R 8 U R O N T 9 N T U R O Consider the given statement/s to be true and decide which of the given conclusions/assumptions can definitely be drawn from the given statement.
Statements: 1. All fish are tortoise.
2. No tortoise is a crocodile.
Conclusion: 1. No crocodile is a fish.
II. No fish is a crocodile.
Consider the given statements to be true and decide which of the given conclusions/assumptions can definitely be drawn from the given statement.
Statements: 1. All books are novels.
2. Some novels are poems.
Conclusions: I. Some books are poems.
II. Some poems are novels.Consider the statement to be true and decide which of the conclusions logically follow:
Statement:
All dogs are animals.
All animals are living beings.
Conclusion
I:Dog is not an animal.
II. Dog is an animal.In the question, a word is represented by only one set of numbers as given in any one of the alternatives. The sets of numbers given in the matrices are represented by two classes of alphabets as in two matrices given below. The columns and rows of Matrix I are numbered from 0 to 4 and that of Matrix II are numbered from 5 to 9. A letter from these matrices can be represented first by its row and next by its column, e.g., 'A' can be represented by 01, 13, etc., and 'S' can be represented by 55, 66, etc. Similarly, you have to identify the set for the word 'BOTH'.
MATRIX I
0 1 2 3 4 0 F A N O I 1 I O F A N 2 A N O I F 3 O F I N A 4 N I A F O MATRIX II
5 6 7 8 9 5 S E H B T 6 H S E T B 7 B T S E H 8 E H T B S 9 T S E H B Consider the given statement/s to be true and decide which of the given conclusions/assumptions can definitely be drawn from the given statement.
Statement I: All astronomers are scientists.
Statement II: Some scientists are shopkeepers.
Conclusion I: All astronomers are shopkeepers.
Conclusion II: All astronomers are scientists.
Conclusion III: Some shopkeepers are astronomers.
Conclusion IV: All scientists are astronomers.A word is represented by only one set of numbers as given in any one of the options. The sets of numbers are formed using two matrices below. The rows and columns of Matrix I are numbered 0 to 4 and Matrix II are numbered 5 to 9. A letter is represented by its row and column numbers. For example, ‘G’ can be coded as 12 or 21, and ‘L’ as 76 or 67.
Find the correct code for the word ‘LIFE’.
Consider the given statement/s to be true and decide which of the given conclusions/assumptions can definitely be drawn from the given statement:
Statements: Some cars are caves.
Conclusion: I. Some cars are not buses
II. Some caves are buses
III. No cave is a bus
IV. Some caves are cars
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.
