In the following question below are given some statements followed by ...
Given Statements:
I. All Z are Y.
II. Some Y are B.
The least possible Venn diagram for the given statement is:
Conclusions:
Conclusion I: False ("Some B are not Z" is not true because there is no negative relation between B and Z. It may be possible but not definitely true. In syllogism, we take the definite cases as true. So this conclusion not follow.)
Conclusion II: False ("Some Y are not Z" is not true because there is no negative relation between Y and Z. It may be possible but not definitely true. So, this conclusion also not follow.)
Conclusion III: True ("Some Z are Y" is true because when all Z are Y is given then "some Z are Y" is also true. Please note that "some" is a subset of "all". For example, when all boys are male, then "some boys are male" is also true.)
So, Only conclusion III follows.
Hence, the correct answer is "Option 3".
In the following question below are given some statements followed by ...
Given Statements:
I. All Z are Y.
II. Some Y are B.
Conclusions:
I. Some B are not Z.
II. Some Y are not Z.
III. Some Z are Y.
Explanation:
Conclusion I:
- From statement I, we know that all Z are Y.
- From statement II, we know that only some Y are B.
- Therefore, it is not possible to definitively conclude that some B are not Z based on the given statements. Conclusion I does not logically follow.
Conclusion II:
- From statement II, we know that some Y are B.
- Since all Z are Y, it is possible that some Y are Z as well.
- Therefore, it is not possible to definitively conclude that some Y are not Z based on the given statements. Conclusion II does not logically follow.
Conclusion III:
- From statement I, we know that all Z are Y.
- Therefore, it logically follows that some Z are Y based on the given statements. Conclusion III logically follows.
Conclusion:
Therefore, only conclusion III follows based on the given statements.
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