Take the statements below to be true, even if they differ from known facts. Which of the conclusions follow logically from them?
Statements:
1. All editors are critics.
2. All editors are speakers.
3. Some students are not critics.
Conclusions:
I. Some critics are speakers.
II. Some students are not editors.
III. Some speakers are not students.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Only conclusions I and II follow
A conclusion follows only if it is true in every diagram that fits the statements; each class named in a statement is taken to have members. “Some X are not Y” cannot be read the other way round.
“All editors are critics”: the circle of editors lies inside the circle of critics
“All editors are speakers”: the circle of editors also lies inside the circle of speakers
“Some students are not critics”: part of the students lies outside the critics; the rest of the students may lie anywhere, even over all the critics and speakers
Conclusion I: Some critics are speakers. — Follows. The editors are critics and also speakers, so at least the editors are critics who are speakers.
Conclusion II: Some students are not editors. — Follows. The students who are not critics cannot be editors, because every editor is a critic.
Conclusion III: Some speakers are not students. — Does not follow. The students may cover all the speakers, as in the diagram; then every speaker is a student.