- Step 1: Break down the premises. The question provides two premises:
- Premise 1: All teachers are educated (teachers are a subset of educated people).
- Premise 2: Some educated people are writers (at least one educated person is a writer).
- Step 2: Analyze logical implications. Since teachers are a subset of educated people, the educated category is broader, implying there are educated people who are not teachers (e.g., doctors, writers). The fact that some educated people are writers does not necessarily involve teachers.
- Step 3: Evaluate the options.
- Option (1): "All teachers are writers" is not guaranteed, as the writers may not include teachers.
- Option (2): "Some teachers are writers" is possible but not certain, as the educated writers could be non-teachers.
- Option (3): "Some educated people are not teachers" must be true, as the broader educated category includes non-teachers.
- Option (4): "No teachers are writers" is not guaranteed, as some teachers could be writers.
- Step 4: Confirm with a Venn diagram. Educated people are a large circle, with teachers as a smaller circle inside. The larger circle includes other educated individuals, confirming some are not teachers.
- Step 5: Verify necessity. Option (3) is the only statement that must be true, as the broader educated category ensures non-teacher educated people exist.
- Step 6: Final conclusion. Option (3) Some educated people are not teachers is the correct answer, as it logically follows from the premises.
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