No poet is a scientist. Some scientists are mathematicians. Which of the following conclusions is valid?
Correct: B
The middle term 'scientists' is distributed in the first premise (No P are S) but undistributed in the second premise (Some S are M). This is the fallacy of the undistributed middle — the syllogism is invalid. No definite conclusion about poets and mathematicians can be drawn. The correct answer is that no valid conclusion follows, but among the given choices, none is logically entailed. However, if forced, 'No poet is a mathematician' does not necessarily follow because some scientists who are mathematicians might not overlap with poets at all. The syllogism as structured is invalid.