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.
Only conclusion II follows
Syllogism Statements and Conclusions Analysis
Let's carefully analyze the given statements and conclusions to determine which conclusion logically follows from the statements.
Understanding the Syllogism Statements
We are given two statements:
- Statement 1: All schools are books.
- Statement 2: No books are papers.
These statements establish relationships between three categories: Schools, Books, and Papers. In syllogism, we treat these statements as absolutely true, regardless of real-world facts.
Analyzing the Conclusions
We need to check if the given conclusions necessarily follow from the statements.
- Conclusion I: No schools are books.
- Conclusion II: Some books are schools.
Detailed Analysis of Conclusion I: No schools are books
Statement 1 explicitly says, "All schools are books." This means that every single entity that is a school is also an entity that is a book. Conclusion I, on the other hand, says "No schools are books," which means there is no overlap between schools and books; they are entirely separate categories. This directly contradicts Statement 1. Therefore, Conclusion I cannot be true based on the given statements.
Detailed Analysis of Conclusion II: Some books are schools
Statement 1 says, "All schools are books." This is a universal affirmative statement. A fundamental rule or inference in logic is that if "All A are B" is true, then "Some B are A" is also true. If all members of the 'schools' group are included within the 'books' group, it means there are some members within the 'books' group that are schools. For example, if all apples are fruits, then certainly some fruits are apples.
Applying this to Statement 1:
- If "All schools are books" is true,
- Then it logically follows that "Some books are schools" is also true.
Therefore, Conclusion II necessarily follows from Statement 1.
Checking for Combined Inference
Statement 1: All Schools → Books
Statement 2: No Books → Papers
From Statement 1 and Statement 2, we can infer that No Schools are Papers (All S are B, No B are P → No S are P). However, the conclusions provided only relate Schools and Books, or Books and Schools, which are relationships directly derived from Statement 1.
Visualizing with Venn Diagrams
We can use Venn diagrams to represent the statements:
| Statement | Venn Diagram Representation |
|---|---|
| All schools are books. | Draw a circle for 'Schools' completely inside a larger circle for 'Books'. |
| No books are papers. | Draw a third circle for 'Papers' completely separate from the 'Books' circle. Since 'Schools' is inside 'Books', the 'Papers' circle will also be separate from the 'Schools' circle. |
Now let's look at the conclusions based on this diagram:
- Conclusion I: No schools are books. The diagram shows the 'Schools' circle is inside the 'Books' circle. This means all schools are books, which is the opposite of "No schools are books". So, Conclusion I is false.
- Conclusion II: Some books are schools. The diagram shows that the 'Schools' circle occupies a part of the 'Books' circle. This area represents things that are both schools and books. Since the area exists (as all schools are books), it means there are some books that are also schools. So, Conclusion II is true.
Conclusion Summary
Based on the analysis of the statements and conclusions, and using logical inference or Venn diagrams:
- Conclusion I ("No schools are books") contradicts Statement 1.
- Conclusion II ("Some books are schools") is a valid inference from Statement 1 ("All schools are books").
Therefore, only Conclusion II follows from the given statements.
Revision Table: Syllogism Rules Applied
| Statement Type | Form | Example | Valid Immediate Inferences (e.g., Conversion) |
|---|---|---|---|
| A (Universal Affirmative) | All S are P | All schools are books. | Conversion by Limitation: Some P are S (Some books are schools). |
| E (Universal Negative) | No S are P | No books are papers. | Simple Conversion: No P are S (No papers are books). |
| I (Particular Affirmative) | Some S are P | Some books are schools. | Simple Conversion: Some P are S (Some schools are books). |
| O (Particular Negative) | Some S are not P | Some books are not papers. | No valid conversion or simple immediate inference. |
In our question, Statement 1 ("All schools are books") is an A-type statement. A valid inference from "All S are P" is "Some P are S". Thus, from "All schools are books", we can infer "Some books are schools". This confirms that Conclusion II follows.
Additional Information on Syllogism and Logic
Syllogism is a type of logical argument that applies deductive reasoning to arrive at a conclusion based on two or more propositions that are asserted or assumed to be true. In a typical categorical syllogism, there are three components:
- Major Premise: A general statement.
- Minor Premise: A specific statement.
- Conclusion: The inference drawn from the two premises.
In this question, Statement 1 and Statement 2 act as the premises. The conclusions are potential inferences we need to evaluate. Syllogism questions test your ability to apply logical rules and structures, not your knowledge of the real world. The truth of the statements within the context of the problem is assumed.
Understanding the four types of categorical propositions (A, E, I, O) and their immediate inferences like conversion, obversion, and contraposition is key to solving syllogism problems. Also, learning about the rules for combining two premises to form a valid conclusion is essential for more complex problems.
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.
Directions: The questions has a statement followed by two conclusions I and II. You have to decide which of the conclusions follows from the given statement and mark your answer as
Statement: Mr A is not among the candidates shortlisted for the post of vice chancellor of a university
Conclusions :
I) Mr. A will be elected as Vice - chancellor
II) Mr. A will not be considered for the post of Vice-chancellor
Read the given statements and conclusions carefully. Assuming that the information in the statements is true, even if it appears to be at variance from commonly established facts, decide which of the conclusions from / logically follows these statements.
Statement:
Poverty makes man hardworking.
Hardworking people are not poor.
Conclusion:
I. A person must be poor to be hardworking.
II. Diligence helps to remove poverty.
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.
