Statements:No mare is a puppy.All puppies are horses.Conclusions: I. All mares are horses.II. Some horses are not mares.OptionsIf only conclusion I followsIf either conclusion I or conclusion II followsIf both conclusion I and conclusion II followsIf neither conclusion I nor conclusion II followsIf only conclusion II follows
Question
Statements:No mare is a puppy.All puppies are horses.Conclusions: I. All mares are horses.II. Some horses are not mares.OptionsIf only conclusion I followsIf either conclusion I or conclusion II followsIf both conclusion I and conclusion II followsIf neither conclusion I nor conclusion II followsIf only conclusion II follows
Solution
The given statements are:
- No mare is a puppy.
- All puppies are horses.
From these statements, we can derive the following:
- Since no mare is a puppy and all puppies are horses, it means that no mare can be a horse that is a puppy.
- However, this does not mean that all mares are horses because there could be horses that are not puppies.
- Also, since all puppies are horses and no mare is a puppy, it means that there are some horses that are not mares (the horses that are puppies).
So, based on these derivations:
Conclusion I: All mares are horses. This conclusion does not follow the given statements.
Conclusion II: Some horses are not mares. This conclusion follows the given statements.
Therefore, the answer is "If only conclusion II follows".
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