PXL_20231028_053356203

(16) Overeating Is foolish only if it causes cancer Overeating does not cause cancer. So, overeating is not foolish (17) Either virtue is good for its own sake, or it is good as a means to an end. It is not the case that virtue is good for its own sake. So, virtue is good as a means to an end. (18) Either virtue is good for its own sake, or it is good as a means to an end. Virtue is good for its own sake. So, virtue is good not as a means to an end. (19) A severe depression will occur if the economy collapses. The economy collapses if inflation soars. So inflation soars only if a severe depression will occur. (20) Euthanasia is morally acceptable only if it promotes a greater amount of happiness for everyone affected than the alternatives do. And euthanasia does promote a greater amount of happiness for everyone affected than the alternatives. Therefore, euthanasia is morally acceptable. P 2. Formalize the following statements (one statement in each question), using the sentence letters provided. (All sentence letters stand for non-negative statement.) (1) The crop will fail if it rains. (C, R) (2) The crop will failwnlEssit#difs. (C, R) (‘Unless’ = ‘if not’ = ‘or otherwise’) (3) Humans are animals if they are mammals. (A, M) (4) Bats are mammals only if they nourish their young with milk. (M, N) (S) Coffeeisn’t good if it isn’t fresh-brewed. (G, F) (6) Assuming that your test score are high and you get your paper in on time, you will do well. (T, P, W) (‘Assuming that’ = ‘if’) (7) Neither birds nor snakes are mammals. (B, S) (8) Al wins only if Ed does not win, and Ed wins only if Al does not win. (A, E) (38) If Smith fails to win then either Jones wins or Smith and Jones are tied. (S, J, 7) (10) Juliois a bachelor if and only if he is a man who is unmarried. (B, M, J: Julio is married) (11) We will be evicted unless we pay the rent. (E, P) (12) Although reindeer exist, Santa does not exist: but adults are not honest if Santa does not exist. (One sentence) (R, S, H) (13) The picture frame is square only if it is rectangular. (S, R) (14) You will not succeed if you lack common sense. (S, C: you have common sense) (15) If Sammy is a penguin, then Sammy is a bird that cannot fly (P, B, F) (16) Either you work hard or you have fun, but not both. (W, F) (17) Neither penguins nor ostriches can fly. (P, O) (18) If Alvin has a bill, then he is not a platypus if he has feathers. (B, P, F) {(18) While Miriam is both competent and hard-working, she is not interested in the job. (C, H, N (20) Assuming that Murphy is a bat only if he can fl%flurphy is not a bat. (B, F) 3. By drawing truth tables, determine whether each of the following formulas is tautologous, truth-functionally contingent, or inconsistent. Place the atomic sentences (alphabetical letters) in the alphabetical order, circle the final columns, and check the rows, if any, which justify your answer, (1) (Pva)—(PeQ)