Exam 3: Inference in Propositional Logic

1. (P $\lor$ ∼R) ⊃ (P ⊃ Q) 2. P $\lor$ ∼R 3. P 4. Q ⊃ ∼S -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 derivable from the given premises using any of the twenty-five rules of PL?

Quinn or Raina will be valedictorian. Quinn's being valedictorian entails that she receives an A+ in Spanish. She doesn't receive an A+ in Spanish. So, Raina is valedictorian. -Which of the following is the best translation into PL of this argument?

I know something if, and only if, I have some causal contact with the physical world. If I know something, then there is no demon deceiver. I know something. So, I know something just in case both I have causal contact with the physical world and there is no demon deceiver. -Working backward from the conclusion of this argument, which of the following is the most likely justification of the last step of the derivation?

translate the given paragraphs into arguments written in PL. Then, derive their conclusions using the rules of inference from section 3.3 (MP, MT, DS, HS, Add, Conj, Simp, CD, DM, Dist, Assoc, Com, DN). -If moral theories measure outcomes or consequences, then they do not concern duty. If trolley cases are compelling, then moral theories measure consequences. Moral theories concern duty. So, trolley cases are not compelling.

derive the conclusions of each of the following arguments using any of the twenty-five rules of PL. -1. (F $\lor$ G) ? H 2. H • ?G 3. F ? I / I

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. L ⊃ M 2. L $\lor$ (M ≡ ∼N) 3. ∼M / N

translate the given paragraphs into arguments written in PL. Then, derive their conclusions using the rules of inference from section 3.2 (MP, MT, DS, HS, Add, Conj, Simp, CD). -Mica goes swimming only if Nicole lifeguards. Pedro is free on the condition that Ona goes to the beach. Mica goes swimming unless Ona goes to the beach. Nicole doesn't lifeguard. So, either Pedro is free or Mica goes swimming.

1. P ⊃ (Q ⊃ R) 2. ∼(R ⊃ S) ⊃ ∼T 3. (U $\lor$ ∼T) $\lor$ ∼(Q ⊃ S) / ∼U ⊃ ∼(P • T) -Which of the following propositions is a likely last line of the indented sequence for an indirect proof nested within an indented sequence for conditional proof for the given argument?

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 ⊃ C) 2. ∼C $\lor$ (D • E) 3. ∼(D $\lor$ F) / ∼A $\lor$ ∼B

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. -(M ⊃ N) ⊃ [(N ⊃ O) ⊃ (M ⊃ O)]

Mica goes swimming only if Nicole lifeguards. Pedro is free on the condition that Ona goes to the beach. Mica goes swimming unless Ona goes to the beach. Nicole doesn't lifeguard. So, either Pedro is free or Mica goes swimming. -Which of the following propositions is an immediate (one-step) consequence in PL of the given premises?

If matter is atomic, then we can observe only modes. If we do not know of the world by pure reason, then, again, we can observe only modes. Either matter is atomic or we do not know of the world by pure reason. So, we can observe only modes. -Which of the following is the best translation into PL of this argument?

1. F ⊃ [(G $\lor$ H) ⊃ I] -Consider assuming 'F' 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?

(A ⊃ B) ⊃ {(C ⊃ D) ⊃ [(∼A ⊃ C) ⊃ (∼D ⊃ B)]} 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. X ⊃ (∼Y $\lor$ Z) 2. ∼X ⊃ (Y $\lor$ Z) 3. ∼Z -Consider assuming '∼X' 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. G ⊃ (H ⊃ I) 2. ∼(J ⊃ I) 3. ∼G ⊃ ∼J -Consider assuming 'G' 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?

[(T ⊃ W) • (X ⊃ W)] ⊃ [(T $\lor$ X) ⊃ W] Which of the following propositions is a proper assumption for conditional proof to prove that the above wff is a logical truth of PL?

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. -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. (C $\lor$ E) $\lor$ D 2. ∼E -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)?