For an E-type universal negative proposition like "No S are P", simple conversion is valid and yields "No P are S". This new statement preserves both the quantity and quality of the original while exchanging subject and predicate. The two propositions express the same exclusion relation between the classes. Hence the correct converted form is "No P are S".
Option A:
Option A, "All P are S", changes both the quantity and the quality of the original statement. It asserts a universal affirmative rather than a universal negative and therefore cannot be logically equivalent to "No S are P".
Option B:
Option B, "Some P are S", asserts an existential particular affirmative that contradicts the universal exclusion in the original. It would claim overlapping membership where the original denies any overlap. Thus it is not a valid conversion.
Option C:
Option C is correct because the conversion of an E proposition simply reverses the positions of subject and predicate while maintaining "no" as the quantifier. This keeps the meaning that the two classes do not share any members, which is consistent with the original statement.
Option D:
Option D, "Some P are not S", changes the form to a particular negative and does not preserve the universal denial of overlap. It allows the possibility that some P are S, which conflicts with the original universal negative.
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