PHL245 H1F
December 4, 2019
Test #4
Alex Koo





























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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.