PHL245 H1F December 4, 2019 Test #4 Alex Koo This test will be scanned and marked on Crowdmark. Please write in something that will show up clearly in a black and white scan. Fill out your information here by PRINTING in CAPITAL LETTERS. Write your name as it appears on Quercus. Do not write anything else on this cover page. Total Marks: 36 For questions 1-6, symbolize the English sentence using the abbreviation scheme provided for each question. 1. Jimmy can not come to Dianne’s cottage unless he (Jimmy) hires at least two cooks. (4) D1: {1} is a cook. B2: {1} can come to {2}. H2: {1} hires {2}. a0: Jimmy. d0: Dianne. f1: The cottage of {1}. 2. Movies that have a celebrity in it are popular. (4) A1: {1} is a movie. D1: {1} is a celebrity. F1: {1} is popular. G2: {1} has {2} in them. NOTE: This sentence is ambiguous. Symbolize it such that the celebrity is a specific or particular celebrity. 3. No student likes exams unless they (the exams) are easy. (4) A1: {1} is a student. D1: {1} is an exam. F1: {1} is easy. L2: {1} likes {2}. 4. Descendants is the best pizza joint
in Toronto, even though it’s expensive. (4) D1: {1} is a pizza joint. E1: {1} is expensive. B2: {1} is better than {2}. G2: {1} is in {2}. a0: Toronto. d0: Descendants. 5. Matt, who is Ben’s dentist, doesn’t like every book that he’s ever read. (4) B1: {1} is a book. F1: {1} is a time. L2: {1} likes {2}. M3: {1} reads {2} at {3}. a0: Matt. b0: Ben. d1: The dentist of {1}. 6. Although Tim only likes his children, only Tim likes his children. (4) D2: {1} is the child of {2}. L2: {1} likes {2}. a0: Tim. 7. Translate the following symbolic sentence into an IDIOMATIC English sentence using the abbreviation scheme provided. (4) y(Dy∧Hy∧H(ay)∧ z(Dz∧Hz∧H(az)∧y≠z∧ w(Dw∧Hw∧H(aw)∧w≠y∧w≠z∧ ~ x(Dx∧Hx∧H(ax)∧x≠y∧x≠z∧x≠w)))) D1: {1} is tricky. H1: {1} is a question. H2: {1} has {2}. a0: Test 4. 8. Show the following argument is valid using a derivation. You may use the basic rules as well as the DERIVED RULES: CDJ, DM, NC, NB, SC, QN, and AV. (8) x y(D(ya(x)b(y))→~ zF(zb(z))). w zD(wwz). ∴ ~ wF(a(a)w) Extra Lines. If you use these, clearly indicate how the grader should read your proof.