Exam 3: Inference in Propositional Logic

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. -Working backward from the conclusion of this argument, which of the following is the most likely justification of the last step of the derivation?

(Multiple Choice)

4.8/5

(34)

Question 221

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. -[(P $\lor$ Q) ⊃ R] ⊃ [S ⊃ (Q ⊃ R)]

(Essay)

4.9/5

(42)

Question 222

1. ∼A ≡ B 2. A • ∼C -Which of the following propositions is derivable from the given premises using any of the twenty-five rules of PL?

(Multiple Choice)

4.9/5

(31)

Question 223

determine whether the given proposition is a logical truth or not. If it is not a logical truth, select a false valuation. -[(W $\lor$ X) ≡ (Y $\lor$ Z)] ⊃ [(W • ∼Y) ⊃ Z]

(Multiple Choice)

4.9/5

(40)

Question 224

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

(Multiple Choice)

4.8/5

(43)

Question 225

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

(Multiple Choice)

4.8/5

(33)

Question 226

determine whether the argument is valid or invalid. If it is invalid, select a counterexample. -1. ∼A $\lor$ B 2) ∼B ⊃ (C ⊃ D) 3) C ≡ ∼D / ∼C

(Multiple Choice)

4.7/5

(29)

Question 227

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. -Working backward from the conclusion of this argument, which of the following is the most likely justification of the last step of the derivation?

(Multiple Choice)

4.7/5

(36)

Question 228

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

(Multiple Choice)

4.9/5

(46)

Question 229

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. -Consider assuming 'E' for indirect proof of the given argument. Which of the following Propositions is a likely last line of the indented sequence?

(Multiple Choice)

4.8/5

(29)

Question 230

1. (E $\lor$ F) ⊃ G 2. J ⊃ (G ⊃ H) 3. ∼(I ⊃ ∼E) -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?

(Multiple Choice)

4.8/5

(36)

Question 231

determine whether the argument is valid or invalid. If it is invalid, select a counterexample. -1. G ⊃ (H $\lor$ I) 2) G ≡ (∼I ⊃ H) / ∼H ⊃ ∼G

(Multiple Choice)

4.9/5

(31)

Question 232

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

(Multiple Choice)

4.8/5

(34)

Question 233

1. F ≡ (G • ∼H) 2. G ≡ (I $\lor$ H) 3. I ⊃ ∼F / ∼F -Which of the following propositions is a likely last line of the indented sequence for an indirect proof of the given argument?

(Multiple Choice)

4.8/5

(36)

Question 234

1. G ⊃ H 2. ∼G ⊃ (I ⊃ J) 3. K ⊃ L 4. I $\lor$ K 5. ∼H -Which of the following propositions is an immediate (one-step) consequence in PL of the given premises?

(Multiple Choice)

4.8/5

(40)

Question 235

1. J ⊃ (K ⊃ M) 2. L $\lor$ ∼M 3. J $\lor$ (K • ∼L) -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?

(Multiple Choice)

4.7/5

(43)

Question 236

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

(Multiple Choice)

4.9/5

(39)

Question 237

1. F ⊃ [(G $\lor$ H) ⊃ I] -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?

(Multiple Choice)

4.9/5

(32)

Question 238

1. P ⊃ (Q ⊃ R) 2. ∼(R ⊃ S) ⊃ ∼T 3. (U $\lor$ ∼T) $\lor$ ∼(Q ⊃ S) / ∼U ⊃ ∼(P • T) -Which of the following methods is most appropriate to derive the conclusion of the given argument?

(Multiple Choice)

4.9/5

(38)

Question 239

determine whether the given proposition is a logical truth or not. If it is not a logical truth, select a false valuation. -(I • K) ⊃ [(I $\lor$ L) • (I $\lor$ M)]

(Multiple Choice)

4.9/5

(38)

Question 240

Showing 221 - 240 of 308

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. -[(P $\lor$ Q) ⊃ R] ⊃ [S ⊃ (Q ⊃ R)]

1. ∼A ≡ B 2. A • ∼C -Which of the following propositions is derivable from the given premises using any of the twenty-five rules of PL?

determine whether the given proposition is a logical truth or not. If it is not a logical truth, select a false valuation. -[(W $\lor$ X) ≡ (Y $\lor$ Z)] ⊃ [(W • ∼Y) ⊃ Z]

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

determine whether the argument is valid or invalid. If it is invalid, select a counterexample. -1. ∼A $\lor$ B 2) ∼B ⊃ (C ⊃ D) 3) C ≡ ∼D / ∼C

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. -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. P ≡ Q 2. ∼Q -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) -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. G ⊃ (H $\lor$ I) 2) G ≡ (∼I ⊃ H) / ∼H ⊃ ∼G

1. F ≡ (G • ∼H) 2. G ≡ (I $\lor$ H) 3. I ⊃ ∼F / ∼F -Which of the following propositions is a likely last line of the indented sequence for an indirect proof of the given argument?

1. G ⊃ H 2. ∼G ⊃ (I ⊃ J) 3. K ⊃ L 4. I $\lor$ K 5. ∼H -Which of the following propositions is an immediate (one-step) consequence in PL of the given premises?

1. J ⊃ (K ⊃ M) 2. L $\lor$ ∼M 3. J $\lor$ (K • ∼L) -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?

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

1. F ⊃ [(G $\lor$ H) ⊃ I] -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. P ⊃ (Q ⊃ R) 2. ∼(R ⊃ S) ⊃ ∼T 3. (U $\lor$ ∼T) $\lor$ ∼(Q ⊃ S) / ∼U ⊃ ∼(P • T) -Which of the following methods is most appropriate to derive the conclusion of the given argument?

determine whether the given proposition is a logical truth or not. If it is not a logical truth, select a false valuation. -(I • K) ⊃ [(I $\lor$ L) • (I $\lor$ M)]

Introducing Logic

Propositional Logic: Syntax and Semantic

Monadic Predicate Logic

Full First-Order Logic

Filters

Exam 3: Inference in Propositional Logic

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. -[(P ∨ \lor ∨ Q) ⊃ R] ⊃ [S ⊃ (Q ⊃ R)]

1. ∼A ≡ B 2. A • ∼C -Which of the following propositions is derivable from the given premises using any of the twenty-five rules of PL?

determine whether the given proposition is a logical truth or not. If it is not a logical truth, select a false valuation. -[(W ∨ \lor ∨ X) ≡ (Y ∨ \lor ∨ Z)] ⊃ [(W • ∼Y) ⊃ Z]

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

determine whether the argument is valid or invalid. If it is invalid, select a counterexample. -1. ∼A ∨ \lor ∨ B 2) ∼B ⊃ (C ⊃ D) 3) C ≡ ∼D / ∼C

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. -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. P ≡ Q 2. ∼Q -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) -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. G ⊃ (H ∨ \lor ∨ I) 2) G ≡ (∼I ⊃ H) / ∼H ⊃ ∼G

1. F ≡ (G • ∼H) 2. G ≡ (I ∨ \lor ∨ H) 3. I ⊃ ∼F / ∼F -Which of the following propositions is a likely last line of the indented sequence for an indirect proof of the given argument?

1. G ⊃ H 2. ∼G ⊃ (I ⊃ J) 3. K ⊃ L 4. I ∨ \lor ∨ K 5. ∼H -Which of the following propositions is an immediate (one-step) consequence in PL of the given premises?

1. J ⊃ (K ⊃ M) 2. L ∨ \lor ∨ ∼M 3. J ∨ \lor ∨ (K • ∼L) -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?

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

1. F ⊃ [(G ∨ \lor ∨ H) ⊃ I] -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. P ⊃ (Q ⊃ R) 2. ∼(R ⊃ S) ⊃ ∼T 3. (U ∨ \lor ∨ ∼T) ∨ \lor ∨ ∼(Q ⊃ S) / ∼U ⊃ ∼(P • T) -Which of the following methods is most appropriate to derive the conclusion of the given argument?

determine whether the given proposition is a logical truth or not. If it is not a logical truth, select a false valuation. -(I • K) ⊃ [(I ∨ \lor ∨ L) • (I ∨ \lor ∨ M)]

Introducing Logic

Propositional Logic: Syntax and Semantic

Monadic Predicate Logic

Full First-Order Logic

Filters

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. -[(P $\lor$ Q) ⊃ R] ⊃ [S ⊃ (Q ⊃ R)]

determine whether the given proposition is a logical truth or not. If it is not a logical truth, select a false valuation. -[(W $\lor$ X) ≡ (Y $\lor$ Z)] ⊃ [(W • ∼Y) ⊃ Z]

determine whether the argument is valid or invalid. If it is invalid, select a counterexample. -1. ∼A $\lor$ B 2) ∼B ⊃ (C ⊃ D) 3) C ≡ ∼D / ∼C

1. (E $\lor$ F) ⊃ G 2. J ⊃ (G ⊃ H) 3. ∼(I ⊃ ∼E) -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. G ⊃ (H $\lor$ I) 2) G ≡ (∼I ⊃ H) / ∼H ⊃ ∼G

1. F ≡ (G • ∼H) 2. G ≡ (I $\lor$ H) 3. I ⊃ ∼F / ∼F -Which of the following propositions is a likely last line of the indented sequence for an indirect proof of the given argument?

1. G ⊃ H 2. ∼G ⊃ (I ⊃ J) 3. K ⊃ L 4. I $\lor$ K 5. ∼H -Which of the following propositions is an immediate (one-step) consequence in PL of the given premises?

1. J ⊃ (K ⊃ M) 2. L $\lor$ ∼M 3. J $\lor$ (K • ∼L) -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. F ⊃ [(G $\lor$ H) ⊃ I] -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. P ⊃ (Q ⊃ R) 2. ∼(R ⊃ S) ⊃ ∼T 3. (U $\lor$ ∼T) $\lor$ ∼(Q ⊃ S) / ∼U ⊃ ∼(P • T) -Which of the following methods is most appropriate to derive the conclusion of the given argument?

determine whether the given proposition is a logical truth or not. If it is not a logical truth, select a false valuation. -(I • K) ⊃ [(I $\lor$ L) • (I $\lor$ M)]