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YOU NEED TO UPLOAD YOUR ANSWERS AS PICTURES. ********************** Pаrt I – Symbоlizаtiоn (50/100 pоints) 1. Symbolize English sentences а–d in PL, and give English readings for e–h, using the following symbolization key (20 points): UD: living things Lxy: x likes y Axy: x is afraid of y Fx: x is friendly Nx: x is a nut-eater Bx: x is a black squirrel Gx: x is a gray squirrel Rx: x is a red squirrel j: Julia a: Aaron a. All gray squirrels are nut-eaters. b. No gray squirrels are nut-eaters. c. Some gray squirrels are nut-eaters. d. Some gray squirrels are not nut-eaters. e. (∃x)(Gx & Fx) & ∼ (∀y)(Gy ⊃ Fy) f. (∀y)[(Gy ∨ Ry) ⊃ Ny] g. (∃x)(∃y)[(Gx & Ry) & Lxy] h. ∼ Ra & (∀y)(Ry ⊃ Lay) 2. Symbolize: Every friendly red squirrel likes Julia.(2 points) (A) (∀x)[(Rx & Fx) & Lxj] (B) (∀x)[Rx ⊃ (Fx & Lxj)] (C) (∀x)[(Rx & Fx) ⊃ Ljx] (D) (∀x)[(Rx & Fx) ⊃ Lxj] 3. Symbolize: Some black squirrel is afraid of every gray squirrel. (2 points) (A) (∃x)(∀y)[(Bx & Gy) ⊃ Axy] (B) (∃x)[Bx & (∀y)(Gy = Axy)] (C) (∃x)[Bx ⊃ (∀y)(Gy ⊃ Ayx)] (D) (∀y)(∃x)[Bx & (Gy ⊃ Axy)] 4. Symbolize: Only nut-eaters like Aaron. (2 points) (A) (∀x)(Nx ⊃ Lxa) (B) (∀x)(Lxa ⊃ Nx) (C) (∃x)(Nx & Lxa) (D) (∀x)(Nx = Lxa) 5. Symbolize: No gray squirrel that is afraid of Julia is friendly. (2 points) (A) (∀x)[Gx ⊃ (Axj & ~Fx)] (B) (∀x)[(Gx & ~Fx) ⊃ Axj] (C) (∀x)[(Gx & Axj) ⊃ ~Fx] (D) ~(∀x)[(Gx & Axj) ⊃ Fx] 6. Symbolize: Every nut-eater is afraid of some red squirrel. (2 points) (A) (∃y)(∀x)[Nx ⊃ (Ry & Axy)] (B) (∀x)(∃y)[(Nx & Ry) & Axy] (C) (∀x)[Nx ⊃ (∃y)(Ry ⊃ Axy)] (D) (∀x)[Nx ⊃ (∃y)(Ry & Axy)] 7. Use the truth-table method to answer the following questions. In each case construct a full truth-table. Be sure to state your results (20 points). a. Is the following sentence truth-functionally true, truth-functionally false, or truth-functionally indeterminate? [(M ∨ ∼ M) = (∼ N ⊃ N)] ∨ (N ⊃ K) b. Is the following set of sentences truth-functionally consistent? {∼ B, D = (B & ∼ D), D ⊃ ∼ B} Part II – Derivations (50/100 points) Provide the justification for lines 1-13 (20 points) Construct the following derivations in PD+ (30 points): a. {(∀x)Gx} |- (∀x)(∼ Gx ⊃ Gx) b. {(∃x)(∀y)Fxy, (∃x)(∀y) ∼ Fxy} |- (∃x)(∃y)Fxy & (∃x)(∃y) ∼ Fxy EXTRA CREDIT: not required; 10 points if (and only if) no important mistake/omission; no partial credit. a. Symbolize: Every gray squirrel likes every friendly squirrel that is afraid of some nut-eater Julia likes - unless Aaron is afraid of that gray squirrel.
Which findings suggest infectiоn? (Select аll thаt аpply)