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
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:
1. Some flowers are chemicals.
2. Some chemicals are herbs.
Conclusions:
I. No flower is a herb.
II. Some flowers are herbs.
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:
All students are teachers.
All teachers are professors.
Conclusions:
1. All students are professors.
2. All professors are students.
3. No teacher is a professor.
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 dentists are surgeons.
II. All the surgeons are doctors.
Conclusions:
I. Some dentists are doctors.
II. No surgeons are dentists.
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 at variance with generally established facts. decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.
Statements:
1) Some angers are griefs.
2) Some griefs are loves.
Conclusion:
I. Some griefs are angers.
II. Some loves are griefsThe statements below are followed by three 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 balls are boats.
All boats are cars.
Conclusions:
I. Some cars are balls.
II. All balls are cars.
III. All cars are balls.
