In the following question below are given some statements followed by ...
Statements:
- All Z are Y: This means every Z is contained within Y.
- Some Y are B: This means there is at least some overlap between Y and B.
Conclusions:
Some B are not Z:
- From the statements, there is no direct evidence that some B are not Z. While we know "Some Y are B" and "All Z are Y," this does not establish anything about the relationship between B and Z. Hence, this conclusion does not follow.
Some Y are not Z:
- From the statement "All Z are Y," it follows that Z is entirely contained within Y. However, nothing in the statements suggests that some Y are not Z. This conclusion does not follow.
Some Z are Y:
- From the statement "All Z are Y," it is clear that all Z are Y, so "Some Z are Y" is logically true as it is part of "all." Hence, this conclusion follows.
c) Only conclusion III follows.
This question is part of UPSC exam. View all CAT courses
In the following question below are given some statements followed by ...
Understanding the Statements
The provided statements are:
- I. All Z are Y.
This means that every element of Z is included in Y.
- II. Some Y are B.
This indicates that there is at least one element that belongs to both Y and B.
Analyzing the Conclusions
Now, we will analyze each conclusion based on the statements:
- Conclusion I: Some B are not Z.
This conclusion cannot be definitively drawn from the statements. Since "Some Y are B" does not imply that those B must be outside of Z, we cannot conclude that some B are not Z.
- Conclusion II: Some Y are not Z.
This conclusion also cannot be confirmed. Since all Z are included in Y, it is possible that all Y could be Z. Hence, we cannot assert that some Y are not Z.
- Conclusion III: Some Z are Y.
This conclusion logically follows from the first statement. Since all elements of Z are included in Y, it is correct to say that some Z must indeed be Y (in fact, all Z are Y).
Final Assessment
Given this analysis, we can conclude:
- Only Conclusion III is valid and logically follows from the statements.
- Conclusions I and II do not logically follow.
Thus, the correct answer is option a) Only conclusion III follows.
However, it seems there was a misunderstanding regarding the correct answer option given in your question. The answer is indeed that only conclusion III follows.