Exam 3: Inference in Propositional Logic

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. (F $\lor$ G) ? H 2. F • E / H

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. (P $\lor$ Q) $\lor$ R 2. ∼(S $\lor$ Q) / ∼P ⊃ R

1. A $\lor$ (B $\lor$ C) 2. B ⊃ D 3. C ⊃ E 4. (D $\lor$ E) ⊃ (A $\lor$ C) 5. ∼A -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)?

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. ?E ? F 2. G • ?E / F

1. ∼P ⊃ (∼Q $\lor$ R) 2. S ⊃ Q -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)?

derive the conclusions of each of the following arguments using any of the twenty-five rules of PL and the direct, conditional, or indirect methods of proof. -1. A ⊃ (B • C) 2. ∼D ⊃ ∼B 3. A / D

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. -Which of the following other 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 derivable from the given premises using the rules available through section 3.2 (MP, MT, DS, HS, Add, Conj, Simp, CD)?

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. -Which of the following is the best translation into PL of this argument?

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. -[(C ⊃ D) • ∼D] ⊃ ∼C

1. J ⊃ K 2. ∼J $\lor$ L 3. (K • L) ≡ M -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. (N ⊃ O) ⊃ P 2. (∼N $\lor$ O) ≡ (∼Q ⊃ R) 3. R $\lor$ (S ⊃ 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?

1. J ⊃ (K ⊃ M) 2. L $\lor$ ∼M 3. J $\lor$ (K • ∼L) -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 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. G ⊃ (H $\lor$ I) 2. G ≡ (∼I ⊃ H) / ∼H ⊃ ∼G

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

1. N $\lor$ (P • ∼R) 2. (P • ∼R) ⊃ Q 3. N ⊃ O 4. ∼O -Which of the following propositions is an immediate (one-step) consequence in PL of the given premises?

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. -Consider assuming 'S' 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?

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. -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. ∼J ⊃ K 2. K ⊃ (L ⊃ M) 3. J ⊃ M 4. ∼M -Which of the following propositions is an immediate (one-step) consequence in PL of the given premises?

derive the conclusions of each of the following arguments 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). -1. (E $\lor$ F) ⊃ (G • H) 2. ∼E ⊃ (D ⊃ ∼D) 3. ∼G $\lor$ ∼H / ∼D