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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 Z are Y.
II. Some Y are B.
Conclusion:
I. Some B are not Z.
II. Some Y are not Z.
III. Some Z are Y.
- a)Both conclusions II and III follows
- b)Both conclusions I and III follows
- c)Only conclusion III follows
- d)All conclusion follows
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
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.
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Community Answer
In the following question below are given some statements followed by ...
Understanding the Statements
The statements provided are:
- I. All Z are Y.
This means every element of Z is also an element of Y.
- II. Some Y are B.
This indicates that there is at least one element that is common between Y and B.
Evaluating the Conclusions
Now, let's analyze each conclusion based on the statements:
- Conclusion I: Some B are not Z.
This conclusion cannot be confirmed based on the given statements. While we know that some Y are B, and all Z are Y, it does not necessarily imply anything about the relationship between B and Z. Therefore, this conclusion does not logically follow.
- Conclusion II: Some Y are not Z.
The statement "All Z are Y" does not imply that all Y must be Z. There could be elements in Y that are not part of Z. Hence, this conclusion cannot be definitively drawn from the given statements.
- Conclusion III: Some Z are Y.
This conclusion is true because all Z are included in Y as stated in the first statement. Therefore, it logically follows that there are some Z that are also Y.
Final Analysis
From the evaluation:
- Only Conclusion III logically follows from the given statements.
- Conclusions I and II do not logically follow based on the information provided.
Thus, the correct answer is option C: Only conclusion III follows.
The statements provided are:
- I. All Z are Y.
This means every element of Z is also an element of Y.
- II. Some Y are B.
This indicates that there is at least one element that is common between Y and B.
Evaluating the Conclusions
Now, let's analyze each conclusion based on the statements:
- Conclusion I: Some B are not Z.
This conclusion cannot be confirmed based on the given statements. While we know that some Y are B, and all Z are Y, it does not necessarily imply anything about the relationship between B and Z. Therefore, this conclusion does not logically follow.
- Conclusion II: Some Y are not Z.
The statement "All Z are Y" does not imply that all Y must be Z. There could be elements in Y that are not part of Z. Hence, this conclusion cannot be definitively drawn from the given statements.
- Conclusion III: Some Z are Y.
This conclusion is true because all Z are included in Y as stated in the first statement. Therefore, it logically follows that there are some Z that are also Y.
Final Analysis
From the evaluation:
- Only Conclusion III logically follows from the given statements.
- Conclusions I and II do not logically follow based on the information provided.
Thus, the correct answer is option C: Only conclusion III follows.
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