Exam 3: Inference in Propositional Logic

If a river is constantly moving and sense experience is veridical, then everything is in flux. If sense experience is veridical, but not our only means of knowledge, then not everything is in flux. So, if a river is constantly moving and sense experience is veridical, then the senses are our only means of knowledge. -Working backward from the conclusion of this argument, which of the following is the most likely justification of the last step of the derivation?

1. A ⊃ B 2. ∼B 3. ∼A ⊃ ∼C -Which of the following propositions is an immediate (one-step) consequence in PL of the given premises?

1. G ⊃ H 2. G ⊃ I -Which of the following propositions is derivable from the given premises using any of the twenty-five rules of PL and either the direct or conditional methods of proof?

1. (A ⊃ B) • (C ⊃ D) 2. E ⊃ A 3. ∼F $\lor$ E 4. ∼∼F -Which of the following propositions is an immediate (one-step) consequence in PL of the given premises?

1. M ≡ ∼N 2. ∼M ⊃ O 3. ∼N ⊃ O -Which of the following propositions is an immediate (one-step) consequence in PL of the given premises?

1. A ⊃ (B $\lor$ ∼C) 2. D ⊃ (∼B • ∼E) -Which of the following propositions is derivable from the given premises using any of the twenty-five rules of PL and either the direct or conditional methods of proof?

translate the given paragraphs into arguments written in PL. Then, derive their conclusions using any of the twenty-five rules of PL and either the direct or conditional methods of proof. -If Sheldon writes a paper, then using the copier is a necessary condition for Yessenia reading it. Yessenia doesn't read it only if Sheldon doesn't write it. So, if Sheldon writes a paper, then he uses the copier.

1. A ⊃ (B ⊃ C) 2. ∼C $\lor$ (D • E) 3. ∼(D $\lor$ F) -Which of the following propositions is derivable from the given premises using the rules available through section 3.4 (MP, MT, DS, HS, Add, Conj, Simp, CD, DM, Dist, Assoc, Com, DN, Cont, Impl, Equiv, Exp, Taut)?

[(C ⊃ D) • ∼D] ⊃ ∼C Which of the following propositions is a proper assumption for conditional proof to prove that the above wff is a logical truth of PL?

If names are purely referential and do not have descriptive content, then 'Fido' means Fido. If names do have descriptive content, then 'Fido' means my idea of Fido. But Fido does not mean my idea of Fido. Names are purely referential. So, 'Fido' means Fido. -Working backward from the conclusion of this argument, which of the following is the most likely justification of the last step of the derivation?

1. (E $\lor$ F) ⊃ (G • H) 2. ∼E ⊃ (D ⊃ ∼D) 3. ∼G $\lor$ ∼H -Which of the following propositions is an immediate (one-step) consequence in PL of the given premises?

(A ⊃ B) ⊃ (∼B ⊃ ∼A) Which of the following propositions is a proper assumption for conditional proof to prove that the above wff is a logical truth of PL?

1. ∼P ⊃ (∼Q $\lor$ R) 2. S ⊃ Q -Which of the following propositions is an immediate (one-step) consequence in PL of the given premises?

determine whether the given proposition is a logical truth of PL or not. If it is a logical truth, provide a proof. If it is not a logical truth, provide a false valuation. -[(G ⊃ H) ⊃ (I ⊃ J)] ⊃ [(G ⊃ I) ⊃ (H ⊃ J)]

Construct a derivation to prove that each of the following propositions is a logical truth of PL using any of the twenty-five rules and conditional proof. -(A ? B) ? (?B ? ?A)

1. (P $\lor$ Q) ⊃ R 2. R ⊃ ∼Q -Which of the following propositions is an immediate (one-step) consequence in PL of the given premises?

determine whether the given proposition is a logical truth or not. If it is not a logical truth, select a false valuation. -[(D ⊃ E) ⊃ F] ⊃ [D ⊃ (E ⊃ F)]

1. (P $\lor$ Q) $\lor$ R 2. ∼(S $\lor$ Q) -Which of the following propositions is an immediate (one-step) consequence in PL of the given premises?

1. P $\lor$ (Q ⊃ R) 2. R ⊃ (S • T) 3. ∼P -Which of the following propositions is derivable from the given premises using the rules of section 3.1 (MP, MT, DS, HS)?

derive the conclusions of each of the following arguments using the rules of inference from section 3.4 (MP, MT, DS, HS, Add, Conj, Simp, CD, DM, Dist, Assoc, Com, DN, Cont, Impl, Equiv, Exp, Taut). -1. A ⊃ ∼B 2. A $\lor$ (B ≡ ∼C) 3. B / ∼C