Exam 3: Inference in Propositional Logic

determine whether the given argument is valid or invalid. If it is valid, provide a derivation of the conclusion from the premises. If it is invalid, provide a counterexample. -1. A ⊃ (B $\lor$ ∼C) 2. A ≡ (B $\lor$ C) / ∼B ⊃ ∼A

determine whether the argument is valid or invalid. If it is invalid, select a counterexample. -1. ∼(R $\lor$ S) 2) ∼R ⊃ (∼T ⊃ X) 3) T ≡ X / T

Julie is considering either occasionalist or epiphenomenal dualism, or identity theory or eliminative materialism. But she can accept neither occasionalist nor epiphenomenal dualism. And she denies identity theory. So, she favors eliminative materialism. -Which of the following is the best translation into PL of this argument?

1. (Z ⊃ W) • (X ⊃ Y) 2. X $\lor$ Z 3. ∼Y / W -Which of the following propositions is a likely last line of the indented sequence for an indirect proof of the given argument?

1. J ⊃ (K $\lor$ L) 2. J ≡ ∼K 3. (∼L $\lor$ M) • (∼L $\lor$ N) -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 the rules of inference from section 3.5 (MP, MT, DS, HS, Add, Conj, Simp, CD, DM, Dist, Assoc, Com, DN, Cont, Impl, Equiv, Exp, Taut). -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.

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

(M ⊃ N) ⊃ [(N ⊃ O) ⊃ (M ⊃ O)] Which of the following propositions is a proper assumption for conditional proof to prove that the above wff is a logical truth of PL?

translate the given paragraphs into arguments written in PL. Then, derive their conclusions using the rules of inference from section 3.1 (MP, MT, DS, HS). -Julie is considering either occasionalist or epiphenomenal dualism, or identity theory or eliminative materialism. But she can accept neither occasionalist nor epiphenomenal dualism. And she denies identity theory. So, she favors eliminative materialism.

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. -Which of the following propositions is an immediate (one-step) consequence in PL of the given premises?

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

1. (E $\lor$ F) ⊃ G 2. J ⊃ (G ⊃ H) 3. ∼(I ⊃ ∼E) -Consider assuming 'J' for conditional proof. Which of the following propositions is an immediate (one-step) consequence in PL of the given premises with that further assumption for conditional proof?

1. (P ⊃ Q) ⊃ R 2. ∼(S ⊃ R) -Which of the following propositions is derivable from the given premises using the rules available through section 3.5 (MP, MT, DS, HS, Add, Conj, Simp, CD, DM, Dist, Assoc, Com, DN, Cont, Impl, Equiv, Exp, Taut)?

1. ∼(N $\lor$ O) 2. P ⊃ ∼Q -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?

determine whether the argument is valid or invalid. If it is invalid, select a counterexample. -1. ∼(M $\lor$ N) 2) ∼M ⊃ (O ⊃ P) 3) O ≡ P / O

1. A ⊃ ∼B 2. A $\lor$ (B ≡ ∼C) 3. B -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)?

derive the conclusions of each of the following arguments using the rules of inference from section 3.2 (MP, MT, DS, HS, Add, Conj, Simp, CD). -1. ?W • ?X 2. Y ? W 3. ?Y ? Z / Z $\lor$ X

derive the conclusions of each of the following arguments using the rules of inference from section 3.2 (MP, MT, DS, HS, Add, Conj, Simp, CD). -1. J ? (K ? L) 2. M ? K 3. M ? J 4. M • K / L • J

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

1. G ⊃ ∼(H $\lor$ I) 2. J $\lor$ G 3. K • H -Which of the following propositions is derivable from the given premises using the rules available through section 3.3 (MP, MT, DS, HS, Add, Conj, Simp, CD, DM, Dist, Assoc, Com, DN)?