In order to incorporate the principles of evidence-based pra…
Questions
In оrder tо incоrporаte the principles of evidence-bаsed prаctice, it is just as important for clinicians as it is for researchers to know which studies provide the strongest and weakest evidence to reject or support different clinical approaches and to recognize strong and weak examples in the literature too.
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.