Select option that is true about the Statements and conclusions given: Statements: All books are papers Some papers are covers Conclusions: I. No cover is book II. Some books are covers
either conclusion I or conclusion II follows
Understanding Syllogism Statements and Conclusions
This question tests your ability to draw logical conclusions from given statements. This type of problem is known as a syllogism. We are given two statements and two conclusions, and we need to determine which conclusion(s) logically follow from the statements.
Analyzing the Given Statements
The statements are:
- All books are papers.
- Some papers are covers.
Let's represent these statements using a simple method like Venn diagrams to visualize the relationships.
Visualizing Statements with Venn Diagrams
Statement 1: All books are papers.
This means the circle representing 'books' is completely inside the circle representing 'papers'.
Statement 2: Some papers are covers.
This means the circle representing 'covers' overlaps with the circle representing 'papers'. However, this overlap could be in the part of 'papers' that is also 'books', or in the part of 'papers' that is not 'books', or both.
Let's consider the possibilities for Statement 2:
- Case 1: The 'some papers are covers' overlap happens only in the part of 'papers' that is NOT 'books'.
- Case 2: The 'some papers are covers' overlap happens in the part of 'papers' that IS 'books' (and potentially also the part that is not 'books').
Evaluating the Conclusions
Now let's look at the conclusions based on these possible cases.
Conclusion I: No cover is book.
- In Case 1 (where covers overlap with papers but not books), this conclusion is true.
- In Case 2 (where covers overlap with papers, and specifically with the part of papers that are books), this conclusion is false, because some books are covers.
Since Conclusion I is true in one possible scenario and false in another, it does not definitely follow from the statements alone.
Conclusion II: Some books are covers.
- In Case 1 (where covers overlap with papers but not books), this conclusion is false, because no books are covers.
- In Case 2 (where covers overlap with papers, and specifically with the part of papers that are books), this conclusion is true, because some books are covers.
Since Conclusion II is true in one possible scenario and false in another, it does not definitely follow from the statements alone.
Analyzing the Relationship Between Conclusions I and II
Notice that Conclusion I ("No cover is book") and Conclusion II ("Some books are covers") are contradictory statements. They cannot both be true at the same time, and they cannot both be false at the same time. If it is true that 'No cover is book', then it must be false that 'Some books are covers'. Conversely, if it is true that 'Some books are covers', then it must be false that 'No cover is book'.
Our analysis of the two cases shows that:
- Case 1 leads to Conclusion I being true and Conclusion II being false.
- Case 2 leads to Conclusion I being false and Conclusion II being true.
This demonstrates that based on the given statements, exactly one of these two conclusions must be true, but we cannot definitively say which one without more information. This situation is described by the phrase "either conclusion I or conclusion II follows".
Final Result
Based on the logical analysis of the statements and the conclusions, we find that either conclusion I or conclusion II must follow.
Important Questions from Conventional Syllogism
In this question, three statements followed by two conclusions numbered I and II have been given. You have to take the given statements to be true even if they seem to be at variance from the commonly facts and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.
Statements: Some flats are apartments.
No apartment is a hall.
Some halls are rooms.
Conclusions: I. At least some rooms are flats.
II. No apartment is a room.
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:
I. Some blue are red.
II. Some green are red.
Conclusions:
I. No blue is green.
II. No red is green.
Given below are two statements, Consider these statements to be true even if they seem factuality absurd, Read the conclusions and then decide which of the given conclusions logically follow(s) from the given statements?
Statements :
1. All vases are flowers.
2. No flowers is a plant.
Conclusions :
1. No vases is a plant.
2. Some plant are vases
In the question two statements are given, followed by three conclusions, I, II and III. 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 : Some cars are scooters.
Statement 2 : All scooters are buses.
Conclusion I : Some scooters are cars.
Conclusion II : Some buses are cars.
Conclusion III : All cars are buses.
In the question below are given three statements followed by two conclusions. You have to take each of the given statements to be true. Read the conclusions and then decide which of the conclusions can be logically derived.
Statements:
Some schools are colleges.
No college is university.
All universities are hospitals.
Conclusions:
I. Some schools are universities.
II. At least some hospitals are colleges.
