2023F T4 with solutions Q

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University of Toronto *

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PHL245

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Computer Science

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Jan 9, 2024

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For questions 1-5, symbolize the sentence using the provided abbreviation scheme. Each question is worth 4 points. 1. Aviva’s father is not Yoona’s best friend, but he (Aviva’s father) is loved by all the kids in the neighborhood. A 1 : {1} is a kid. B 2 : {1} is in {2}. L 2 : {1} is loved by {2}. a 0 : Aviva. d 0 : Yoona. g 0 : The neighborhood. b 1 : The best friend of {1}. f 1 : The father of {1}. f(a) ≠b(d) ∧ ∀x(Ax∧B(x g )→L(f(a)x )) (Ax→(B(x g )→L(f(a)x ))) NOTE: You can use b(d) instead of f(a) in the L predicate NOTE: You cannot put the inequality within the scope of the universal 2. Some person in Toronto doesn’t like any radio stations broadcasted from Buffalo. A 1 : {1} is a person. D 1 : {1} is a radio station. F 2 : {1} is in {2}. G 2 : {1} is broadcasted from {2}. L 2 : {1} likes {2}. a 0 : Toronto. b 0 : Buffalo ∃x(Ax∧F(xa)∧∀y(Dy∧G(yb)→~L(xy)) ) →(G(yb)→ ~∃y(Dy∧G(yb)∧L(xy)) NOTE: In this form you can introduce the radio stations �irst 3. Everyone enrolled in PHL245 other than Ming drinks a cup of coffee in the morning. A 1 : {1} is a person. D 1 : {1} is a cup of coffee. B 2 : {1} is enrolled in {2}. F 2 : {1} drinks {2} in the morning. g 0 : Ming. h 0 : PHL245. ∀x(Ax∧B(xh)∧x g→∃y(Dy∧F(xy))) ∧ Ag∧B(gh) Brackets around this part are optional NOTE: This is technically ambiguous. You can start this with the ∃ for the coffee, and it will then mean that everyone other than Ming drinks the SAME cup of coffee. We will accept that.
4. Steve doesn’t like gardens unless there are at least two �lowers in them. F 1 : {1} is a �lower. G 1 : {1} is a garden. L 2 : {1} likes {2}. M 2 : {1} is in {2}. a 0 : Steve. ∀x(Gx → (∼ L(ax) ∨ ∃y∃z(Fy ∧ Fz ∧ y≠ z ∧ M(yx) ∧ M(zx)))) ∀x(Gx ∧ L(ax) → ∃y∃z(Fy ∧ Fz ∧ y≠z ∧ M(yx) ∧ M(zx))) ∀x(Gx →(L(ax)→ ∀x(Gx→ (~AT LEAST TWO→~L(ax))) ∀x(Gx∧~AT LEAST TWO → ~L(ax)) 5. The slowest car on the 401 has at least one chip in its windshield. A 1 : {1} is a chip. D 1 : {1} is a car. B 2 : {1} is on {2}. F 2 : {1} is slower than {2}. L 2 : {1} is in the windshield of {2}. a 0 : The 401. ∃x(Dx∧B(xa)∧∀y(Dy∧B(ya)∧x≠y→F(xy))∧∃z(Az∧L(zx))) Can swap things around lots. Be careful of scope errors. Biconditional Form: ∃x(∀y(Dy∧B(ya)↔x=y)∧∃z(Az∧L(zx))) 6. Translate the following symbolic sentence into an IDIOMATIC English sentence using the abbreviation scheme provided. (4) ∀x(Ax∧B(xf)∧D(xa)→∀y(Ay∧B(yf)∧D(ya)→∀z(Az∧B(zf)∧D(za)→z=x∨z=y))) A 1 : {1} is a song. B 2 : {1} is on {2}. D 2 : {1} is despised by {2}. a 0 : Rheya. f 0 : The kid’s playlist. At most two songs on the kid’s playlist are despised by Rheya. Rheya despises at most two…
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