Select the correct answerStatements:Some lecturers are teachers.Some teachers are professors.Conclusions:I. Some lecturers are professors.II. No lecturer is a professor.OptionsIf only conclusion II followsIf only conclusion I followsIf both conclusion I and conclusion II followsIf either conclusion I or conclusion II followsIf neither conclusion I nor conclusion II follows
Question
Select the correct answerStatements:Some lecturers are teachers.Some teachers are professors.Conclusions:I. Some lecturers are professors.II. No lecturer is a professor.OptionsIf only conclusion II followsIf only conclusion I followsIf both conclusion I and conclusion II followsIf either conclusion I or conclusion II followsIf neither conclusion I nor conclusion II follows
Solution
The correct answer is "If neither conclusion I nor conclusion II follows".
Here's why:
The two statements given are:
- Some lecturers are teachers.
- Some teachers are professors.
From these two statements, we cannot definitively conclude that "Some lecturers are professors" (Conclusion I) or "No lecturer is a professor" (Conclusion II).
The first conclusion assumes that there is an overlap between the lecturers and professors through the common group of teachers. However, the statements do not confirm this overlap. The lecturers who are teachers could be completely different from the teachers who are professors.
The second conclusion assumes that there is no overlap at all between lecturers and professors. But the statements do not confirm this either. It's possible that some lecturers could also be professors.
Therefore, neither conclusion follows from the given statements.
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