(1) Joe lives in a fraternity.(2) Freshmen are not allowed to live in fraternities.(3) Joe is not a freshman.(4) Joe has not declared a major.(5) Joe is not a senior.(6) I never met Joe before today.(7) If Joe were a junior, I would have met him before today.(8) Joe is not a junior.______________________∴(9) Joe is a sophomore.

(1) Joe lives in a fraternity.(2) Joe is allowed to live where he lives. (suppressed premise)(3) Freshmen (first-year students) are not allowed to live in fraternities.______________________∴(4) Joe is not a freshman.(5) Joe has not declared a major.(6) All seniors (fourth-year students) have declared a major. (suppressed premise)______________________∴(7) Joe is not a senior.(8) I never met Joe before today.(9) If Joe were a junior (third-year student), then I would have met him before today.______________________∴(10) Joe is not a junior.(11) Joe is either a freshman, a sophomore, a junior, or a senior. (suppressed premise)______________________∴(12) Joe is a sophomore (second-year student). (from 4, 7, 10, and 11)

(1) Joe lives in a fraternity.(2) Joe is allowed to live where he lives. (suppressed premise)(3) Freshmen (first-year students) are not allowed to live in fraternities.______________________∴(4) Joe is not a freshman.______________________∴(5) Joe is a sophomore (second-year student).(6) Joe has not declared a major.(7) All seniors (fourth-year students)have declared a major. (suppressed premise)______________________∴(8) Joe is not a senior.______________________∴(9) Joe is a sophomore.(10) I never met Joe before today.(11) If Joe were a junior (third-year student), then I would have met him before today.______________________∴(12) Joe is not a junior.______________________∴(13) Joe is a sophomore.