In the following question below are given some statements followed by ...
Analyzing the Conclusions:
-
Some B are not Z –
- From the first statement, we know that all Z are Y, but it does not imply that all Y are Z. The second statement tells us that some Y are B. Since Z is a subset of Y, and there’s no restriction saying that B can’t be outside of Z, we cannot conclusively say that some B are not Z. It’s possible that the intersection of B and Y could be completely within Z, meaning no B is outside of Z.
- Therefore, this conclusion does not necessarily follow.
-
Some Y are not Z –
- We know from Statement I that all Z are Y, but not all Y are Z (because Z is a subset of Y, but not the entire set of Y). Therefore, it’s possible that some Y are not Z.
- This conclusion does follow.
-
Some Z are Y –
- Since all Z are Y (Statement I), it’s obvious that every Z is a Y. Therefore, this conclusion is automatically true.
Conclusion:
- Conclusion I (Some B are not Z) does not necessarily follow.
- Conclusion II (Some Y are not Z) does follow.
- Conclusion III (Some Z are Y) follows because all Z are Y.
Correct Answer:
- c) Both conclusions II and III follow.
View all questions of this test
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.