The statement below is followed by three conclusions labelled I, II and III. You have to assume everything in the statement to be true, and then decide which of the three suggested conclusions logically follows for pursuing. Statements: 1) No school is an institution but they are establishment. 2) All establishments that are not institutions have buildings. Conclusions: I. Schools are not establishments. II. All schools have buildings.
Only conclusion II follows
Analyzing Logical Reasoning Statements and Conclusions
This question asks us to analyze two statements and determine which of the given conclusions logically follows from them. We must assume the statements are true, even if they contradict common knowledge. This is a classic logical deduction problem.
Step-by-Step Analysis of Statements and Conclusions
Let's break down the given statements and conclusions carefully.
Statement 1: No school is an institution but they are establishment.
- This statement has two parts:
- Part 1: No school is an institution. This tells us that the set of schools and the set of institutions have no overlap.
- Part 2: Schools are establishments. This tells us that the set of schools is a subset of the set of establishments. Every school is an establishment.
Statement 2: All establishments that are not institutions have buildings.
- This statement refers to a specific group within the set of establishments: those establishments that are NOT institutions.
- It says that every single member of this specific group (establishments that are not institutions) possesses buildings.
Now let's evaluate each conclusion based on these statements.
Conclusion I: Schools are not establishments.
- Look back at Statement 1. The second part explicitly states, "they are establishment", where "they" refers to schools.
- This means Statement 1 says schools are establishments.
- Conclusion I contradicts Statement 1.
- Therefore, Conclusion I does not follow.
Conclusion II: All schools have buildings.
- From Statement 1, we know that schools are establishments.
- From Statement 1, we also know that no school is an institution.
- Combining these two points, schools are establishments that are not institutions.
- Now look at Statement 2: "All establishments that are not institutions have buildings."
- Since schools are establishments that are not institutions, and all such establishments have buildings, it logically follows that schools must have buildings.
- Therefore, Conclusion II logically follows from the statements.
Conclusion III: Schools do not have buildings.
- Our analysis for Conclusion II showed that, based on the statements, schools must have buildings.
- Conclusion III says the opposite: schools do not have buildings.
- This conclusion contradicts the logical deduction from the statements.
- Therefore, Conclusion III does not follow.
Summary of Conclusions
Based on the logical analysis:
- Conclusion I: Does not follow.
- Conclusion II: Logically follows.
- Conclusion III: Does not follow.
Only Conclusion II logically follows from the given statements.
Analyzing the Options
Let's check the given options against our finding that only Conclusion II follows.
| Option | Description | Matches our findings? |
|---|---|---|
| 1 | Only conclusion III follows | No (Conclusion III does not follow) |
| 2 | Either conclusion I or II follow | No (Only II follows, I does not) |
| 3 | Only conclusion I follows | No (Conclusion I does not follow) |
| 4 | Only conclusion II follows | Yes (Exactly matches our finding) |
Option 4 correctly states that only conclusion II follows.
Final Logical Deduction
The statements establish a relationship between Schools, Institutions, Establishments, and Buildings. Schools are a type of Establishment that are not Institutions. Statement 2 gives a property to all such Establishments (that are not Institutions) - they have buildings. Since schools fall into this category, they must have buildings.
Revision Table: Logical Reasoning Key Points
| Concept | Explanation | Relevance to Problem |
|---|---|---|
| Logical Deduction | inferring conclusions strictly from given premises (statements). | The core process used to solve the problem. |
| Assuming Statements are True | Accepting the given statements as factual, regardless of real-world accuracy. | Crucial rule for solving these types of logical reasoning questions. |
| Contradiction | A conclusion that opposes or denies the statements or deductions from them. | Conclusion I and III contradict the statements or logical deductions. |
| Set Theory Basics (Implicit) | Understanding relationships like 'No A is B', 'All A are B', 'A are B but not C'. | Helps visualize the relationships between Schools, Institutions, and Establishments. |
Additional Information: Types of Logical Reasoning Problems
Logical reasoning is a common section in many exams. Problems can come in various forms:
- Syllogisms: Like this question, involving statements relating categories (e.g., All A are B, Some B are C) and asking which conclusions follow. Can involve two or more statements.
- Statement and Assumptions: A statement is given, followed by assumptions. You decide which assumption is implicit in the statement.
- Statement and Arguments: A statement is given, followed by arguments for or against it. You decide which arguments are strong or weak.
- Statement and Course of Action: A situation (statement) is given, followed by possible actions. You decide which course of action is most appropriate.
- Puzzles: Involving deduction from a set of clues to figure out arrangements, relationships, etc.
For statement and conclusion problems, Venn diagrams can sometimes be a helpful tool to visualize the relationships described in the statements and test the validity of the conclusions, although careful verbal analysis as shown above is often sufficient and sometimes more precise, especially with 'No' statements.
Important Questions from Statements and Conclusions
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. All A are B.
II. Some B are C.
Conclusions:
I. Some A are C.
II. Some A are not C.
III. Some A are B.
Read the given statements and conclusions carefully and decide which of the given conclusions logically follows from the given statements.
Statement:
A asked C, "What time is it now?" Is it half past two? ''
Conclusions:
1. A wants to go to lunch.
2. A wants to confirm what the time is because his watch is off.
In the question one statement is given, followed by two conclusions, I and II. You have to consider the statements to be true even if it seems to be at variance from commonly known facts. You have to decide which of the given conclusions, if any, follows from the given statements.
Statement : 55% of Manisha's office colleagues went to watch the movie.
Conclusion I : Manisha went to watch the movie.
Conclusion II : Manisha did not go to watch the movie.
In the question two statements are given, followed by two conclusions, I and II. You have to consider the statements to be true even if it seems to be at variance from commonly known facts. You have to decide which of the given conclusions, if any, follows from the given statements.
Statement 1 : All schools are books.
Statement 2 : No books are papers.
Conclusion I : No schools are books.
Conclusion II : Some books are schools.
In the question below are given some statements followed by some conclusions based on those statements. Take the given statements to be true even if they seem to be different from commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements.
Statements:
I. Some P are Q.
II. All P are N.
Conclusion:
I. All Q are N.
II. Some P are not Q.
