Exam 3: Inference in Propositional Logic

1. A ⊃ (B • C) 2. ∼D ⊃ ∼B 3. A / D -Which of the following propositions is a likely last line of the indented sequence for an indirect proof of the given argument?

1. A ≡ ∼(B $\lor$ C) 2. ∼D ≡ (A • E) 3. (D ⊃ B) • (E ⊃ B) -Consider assuming 'B' 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?

determine whether the given proposition is a logical truth or not. If it is not a logical truth, select a false valuation. -[A ⊃ (B ⊃ C)] ⊃ [(A ⊃ B) ⊃ (∼C ⊃ A)]

derive the conclusions of each of the following arguments using the rules of inference from section 3.1 (MP, MT, DS, HS). -1. T ? S 2. S ? R 3. T / R

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. J $\lor$ (M $\lor$ L) 2. (∼J ⊃ M) ⊃ K 3. K ⊃ N 4. ∼J • ∼L / N

derive the conclusions of each of the following arguments using the rules of inference from section 3.3 (MP, MT, DS, HS, Add, Conj, Simp, CD, DM, Dist, Assoc, Com, DN). -1. G ⊃ ∼(H $\lor$ I) 2. J $\lor$ G 3. K • H / J • K

derive the conclusions of each of the following arguments using the rules of inference from section 3.1 (MP, MT, DS, HS). -1. P $\lor$ (Q ? R) 2. R ? (S • T) 3. ?P / Q ? (S • T)

translate the given paragraphs into arguments written in PL. Then, derive their conclusions using any of the twenty-five rules of PL and the direct, conditional, or indirect methods of proof. -Either arithmetic and logic are both necessary or logic and geometry are both necessary. If all knowledge is experiential, then even logic is not necessary. So, not all knowledge is experiential.

Owen will be happier if, and only if, he either practices the cello or quits music lessons. It is not that case that Owen quits music lessons only if he'll be happier. So, it is not the case that he both never sleeps and doesn't practice. -Which of the following is the best translation into PL of this argument?

provide a proof of the given logical truth using any of the twenty-five rules of PL and the direct, conditional, or indirect methods of proof. -[(P ⊃ Q) ⊃ Q] ⊃ (P $\lor$ Q)

1. (F $\lor$ G) ⊃ H 2. F • E -Which of the following propositions is not derivable from the given premises using the rules available through section 3.2 (MP, MT, DS, HS, Add, Conj, Simp, CD)?

derive the conclusions of each of the following arguments using any of the twenty-five rules of PL. -1. (J ? K) $\lor$ L 2. K ? L 3. ?L / ?J

It is not the case that if aesthetic values are objective, then we must treat them as such. So, aesthetic values are objective just in case it is not the case that we must treat them as such. -Which of the following is the best translation into PL of this argument?

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. -(I • K) ⊃ [(I $\lor$ L) • (I $\lor$ M)]

translate the given paragraphs into arguments written in PL. Then, derive their conclusions using any of the twenty-five rules of PL. -The dentist is pleased if, and only if, I both brush and floss. The dentist is not pleased, but I brush. So, I don't floss.

derive the conclusions of each of the following arguments using the rules of inference from section 3.1 (MP, MT, DS, HS). -1. A ? B 2. ?B 3. ?A ? ?C / ?C

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

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

1. M ⊃ J 2. M ⊃ (J ⊃ K) 3. J ⊃ (K ⊃ L) -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)?

If neuroscience makes progress, then the mind is the brain. If the mind is soul-like, then rational thought is inexplicable. If neuroscience does not progress, then the mind is soul- like. If philosophy of mind is vacuous, then the mind is not the brain and rational thought is explicable. So, philosophy of mind is not vacuous. -Which of the following is the best translation into PL of this argument?