Joe is not a freshman, since he lives in a fraternity, and freshmen are not allowed to live in fraternities. He also can’t be a senior, since he has not declared a major. And he can’t be a junior, because I never met him before today, and I would have met him before now if he were a junior. So Joe must be a sophomore. Which of the following is the best reconstruction? (1) (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. (2) (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) (3) (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.