2023F MU solutions Q

For questions 1-4, symbolize the sentence using the provided abbreviation scheme. Each question is worth 4 points. 1. Smart watches, which are overpriced, and smart phones that are not made by Apple are useful. A 1 : {1} is a smart watch. D 1 : {1} is a smart phone. G 1 : {1} is useful. H 1 : {1} is overpriced. M 2 : {1} is made by {2}. a 0 : Apple. ∀x(Ax→Hx) ∧ ∀x(Ax∨(Dx∧~M(xa))→Gx) NOTE: We will accept if your answer also says that the smart watch is not made by Apple 2. At most one athlete will cheat at the tournament. A 1 : {1} is an athlete. D 2 : {1} will cheat at {2}. g 0 : The tournament. ∀x(Ax∧D(xg)→∀y(Ay∧D(yg)→x=y)) ~∃y(Ay∧D(yg)∧x ≠ y)) 3. The gardener standing between Steve and Sarah is taller than both of them. G 1 : {1} is a gardener. K 2 : {1} is taller than {2}. B 3 : {1} is standing between {2} and {3}. a 0 : Steve. b 0 : Sarah. ∃x((Gx ∧ B(xab) ∧ ∀y(Gy ∧ B(yab) → y = x)) ∧ K(xa) ∧ K(xb)) 4. Among yellow �lowers , only sun�lowers will grow in Sarah’s garden unless Steve helps her weed it (Sarah’s garden). F 1 : {1} is �lower. H 1 : {1} is yellow. J 1 : {1} is a sun�lower. M 2 : {1} will grow in {2}. A 3 : {1} helps {2} weed {3}. f 1 : The garden of {1}. a 0 : Steve. b 0 : Sarah. ∀x(Fw∧Hx→(M(xf(b)) →Jx))∨A(abf(b)) 5. Translate the following symbolic sentence into an IDIOMATIC English sentence using the abbreviation scheme provided. (4) (Af∧B(�h)∧∃y(Dy∧Gy∧M(fy))) ∧ ∀x(Ax∧B(xh)∧x≠f→~∃y(Dy∧Gy∧M(xy))) A 1 : {1} is a person. D 1 : {1} is a sandwich. G 1 : {1} is good. B 2 : {1} is in {2}. M 2 : {1} makes {2}. f 0 : Vilda. h 0 : Toronto.

Vilda is the only person in Toronto who makes a good sandwich. The only person in Toronto who makes a good sandwich is Vilda Exactly one person in Toronto makes a good sandwich, and that person is Vilda. Vilda is a person in Toronto who makes a good sandwich and no one else in Toronto makes a good sandwich. 6. Provide a Shortened Truth Table that demonstrates that the following argument is invalid. Do so by �illing in the table provided. (4) ~( R ∨P↔W∨Q). Q∨~( R ∨W). ∴ (~ R ∨P)→(W↔(Q∧P)) P Q R W ANSWER: P Q R W F T F T 7. Show that the following argument is valid using a Derivation. You may use only the BASIC RULES: R, MP, MT, ADD, MTP, ADJ, S, DN, CB, and BC; and UI, EI, and EG. (10) ∃xM(xb(x))→∀w∃z(Fz∧Gw). ∃x∀y(~Aa(x)∨M(xy)). ∴ ∀zAz→∃y(Gy∧Fy)