Exam 3: Inference in Propositional Logic

1. ∼W • ∼X 2. Y ⊃ W 3. ∼Y ⊃ Z -Which of the following propositions is derivable from the given premises using the rules available through section 3.2 (MP, MT, DS, HS, Add, Conj, Simp, CD)?

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

[(P $\lor$ Q) ⊃ R] ⊃ [S ⊃ (Q ⊃ R)] 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. (U • Y) ⊃ Z 2. ∼Z -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?

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 ⊃ C) ⊃ (D ⊃ E) 2. A ⊃ B 3. B ⊃ C / ∼E ⊃ ∼D

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

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. -[A ⊃ (B ⊃ C)] ⊃ [(A ⊃ B) ⊃ (∼C ⊃ A)]

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