Analyze the given statements and decide which of the conclusions logically follow, assuming the statements to be true even if they contradict general facts.
Statements:
No Apple is an Orange.
Some Fruits are Oranges.
All Berries are Fruits.
Conclusions:
I. Some Fruits are not Apples.
II. Some Fruits are Apples.
Correct Answer :
Only I follows
Solution :
The correct option is Only I follows.
Step-by-Step Explanation:
Let us analyze the given statements and conclusions using logical deduction or Venn diagrams:
Given Statements:
1. No Apple is an Orange.
2. Some Fruits are Oranges (which means Some Oranges are Fruits).
3. All Berries are Fruits.
Evaluating Conclusion I: Some Fruits are not Apples.
From statement 2, we know that there are some Fruits that are Oranges (the overlap between Fruits and Oranges).
From statement 1, we know that no Apple can be an Orange (Oranges and Apples are completely disjoint sets).
Therefore, those specific Fruits that are Oranges can never be Apples.
Hence, Conclusion I logically follows.
Evaluating Conclusion II: Some Fruits are Apples.
The statements give no information asserting a positive relation between Fruits and Apples. While it might be possible, it is not a definite conclusion derived strictly from the given premises.
Hence, Conclusion II does not follow.
Therefore, only conclusion I logically follows from the given statements.
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