Question

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 1

The correct option is B Some teachers are not mathematicians.

The statement to be a teacher one must graduate from college is A -type and we can write it as, all teachers are college graduates.
Statement I: All teachers all college graduates (A)
Statement IV: No college graduate is poor (E)
Conclusion A +E =E type
No college graduate is poor...(i)
So, option (3) is valid.
Statement IV: No college graduate is poor (E)
Conclusion of statement II: All poor are poets (A)
Conclusion: E +A =E type
No college graduate that is a teacher, is a poet. From this, we may draw the conclusion that poets are not teachers.
So, Option (4) is valid.
Statement III: Some mathematicians are poets (I)
Statement II: All poets are poor (A)
Conclusion: I +A =I type
Some mathematicians are poor. From (1), no college graduate is poor.
From above two conclusions, we can say that some teachers are not mathematicians.