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Discussion

Consider the following argument :

"In order to be a teacher, one must graduate from college. All poets are poor. Some Mathematicians are poets. No college graduate is poor." Which one of the following is not a valid conclusion regarding the above argument ?

  • A.Some Mathematicians are not teachers.
  • B.Some teachers are not Mathematicians.
  • C.Teachers are not poor.
  • D.Poets are not teachers.

Answer: B

The conclusion that is not valid is Some teachers are not Mathematicians.

From the premises: every teacher is a graduate, no graduate is poor, so no teacher is poor (option c follows). All poets are poor, so no poet is a graduate and hence no poet is a teacher (option d follows). Some mathematicians are poets, and those cannot be teachers, so some mathematicians are not teachers (option a follows).

Nothing in the argument says anything about teachers who are not mathematicians; all teachers might be mathematicians who are not poets. So option (b) does not follow.

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