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. -[(T ⊃ W) • (X ⊃ W)] ⊃ [(T $\lor$ X) ⊃ W]

(Essay)

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Question 21

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. (F • ∼ G) ⊃ H 2. J $\lor$ F 3. ∼G • ∼I 4. ∼J / H $\lor$ I

(Essay)

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Question 22

translate the given paragraphs into arguments written in PL. Then, derive their conclusions 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). -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 only observe modes.

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Question 23

1. (P $\lor$ Q) $\lor$ R 2. ∼(S $\lor$ Q) -Which of the following propositions is derivable from the given premises using the rules available through section 3.4 (MP, MT, DS, HS, Add, Conj, Simp, CD, DM, Dist, Assoc, Com, DN, Cont, Impl, Equiv, Exp, Taut)?

(Multiple Choice)

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Question 24

1. (A ⊃ C) ⊃ (D ⊃ E) 2. A ⊃ B 3. B ⊃ C -Which of the following propositions is derivable from the given premises using the rules available through section 3.4 (MP, MT, DS, HS, Add, Conj, Simp, CD, DM, Dist, Assoc, Com, DN, Cont, Impl, Equiv, Exp, Taut)?

(Multiple Choice)

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Question 25

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. ∼(I $\lor$ J) 2. J ⊃ (K ⊃ L) 3. K ≡ ∼L / L

(Essay)

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Question 26

derive the conclusions of each of the following arguments using the rules of inference from section 3.1 (MP, MT, DS, HS). -1. ?J ? K 2. K ? (L ? M) 3. J ? M 4. ?M / ?L

(Essay)

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Question 27

1. G ⊃ H 2. G ⊃ I -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?

(Multiple Choice)

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Question 28

1. (A ⊃ C) ⊃ (D ⊃ E) 2. A ⊃ B 3. B ⊃ C -Which of the following propositions is an immediate (one-step) consequence in PL of the given premises?

(Multiple Choice)

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Question 29

translate the given paragraphs into arguments written in PL. Then, derive their conclusions using the rules of inference from section 3.1 (MP, MT, DS, HS). -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.

(Essay)

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Question 30

[F ⊃ (G $\lor$ H)] ⊃ [∼G ⊃ (F ⊃ H)] Which of the following propositions is a proper assumption for conditional proof to prove that the above wff is a logical truth of PL?

(Multiple Choice)

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Question 31

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. I • (J $\lor$ H) 2. I ⊃ ∼J 3. H ≡ (K $\lor$ I) / K

(Essay)

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Question 32

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

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Question 33

determine whether the argument is valid or invalid. If it is invalid, select a counterexample. -1. J $\lor$ (M $\lor$ L) 2) (∼J ⊃ M) ⊃ K 3) K ⊃ N 4) ∼J • ∼L / N

(Multiple Choice)

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Question 34

1. N ⊃ ∼O 2. P ⊃ ∼Q 3. (N $\lor$ P) $\lor$ R 4. ∼R -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)?

(Multiple Choice)

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Question 35

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 $\lor$ O 2. Q ⊃ ∼O / ∼Q $\lor$ P

(Essay)

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Question 36

1. L ⊃ M 2. L $\lor$ (M ≡ ∼N) 3. ∼M -Which of the following propositions is derivable from the given premises using the rules available through section 3.4 (MP, MT, DS, HS, Add, Conj, Simp, CD, DM, Dist, Assoc, Com, DN, Cont, Impl, Equiv, Exp, Taut)?

(Multiple Choice)

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Question 37

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). -If names are purely referential and do not have descriptive content, then 'Fido' means Fido. If names do have descriptive content, then 'Fido' means my idea of Fido. But Fido does not mean my idea of Fido. Names are purely referential. So, 'Fido' means Fido.

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Question 38

1. (F • ∼ G) ⊃ H 2. J $\lor$ F 3. ∼G • ∼I 4. ∼J / H $\lor$ I -Which of the following propositions is a likely last line of the indented sequence for an indirect proof of the given argument?

(Multiple Choice)

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Question 39

1. G ⊃ H 2. ∼G ⊃ (I ⊃ J) 3. K ⊃ L 4. I $\lor$ K 5. ∼H -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)?

(Multiple Choice)

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Question 40

Showing 21 - 40 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. -[(T ⊃ W) • (X ⊃ W)] ⊃ [(T $\lor$ X) ⊃ W]

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. (F • ∼ G) ⊃ H 2. J $\lor$ F 3. ∼G • ∼I 4. ∼J / H $\lor$ I

1. (P $\lor$ Q) $\lor$ R 2. ∼(S $\lor$ Q) -Which of the following propositions is derivable from the given premises using the rules available through 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 -Which of the following propositions is derivable from the given premises using the rules available through section 3.4 (MP, MT, DS, HS, Add, Conj, Simp, CD, DM, Dist, Assoc, Com, DN, Cont, Impl, Equiv, Exp, Taut)?

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. ∼(I $\lor$ J) 2. J ⊃ (K ⊃ L) 3. K ≡ ∼L / L

derive the conclusions of each of the following arguments using the rules of inference from section 3.1 (MP, MT, DS, HS). -1. ?J ? K 2. K ? (L ? M) 3. J ? M 4. ?M / ?L

1. G ⊃ H 2. G ⊃ I -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?

1. (A ⊃ C) ⊃ (D ⊃ E) 2. A ⊃ B 3. B ⊃ C -Which of the following propositions is an immediate (one-step) consequence in PL of the given premises?

[F ⊃ (G $\lor$ H)] ⊃ [∼G ⊃ (F ⊃ H)] Which of the following propositions is a proper assumption for conditional proof to prove that the above wff is a logical truth of PL?

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. I • (J $\lor$ H) 2. I ⊃ ∼J 3. H ≡ (K $\lor$ I) / K

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

1. N ⊃ ∼O 2. P ⊃ ∼Q 3. (N $\lor$ P) $\lor$ R 4. ∼R -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)?

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 $\lor$ O 2. Q ⊃ ∼O / ∼Q $\lor$ P

1. L ⊃ M 2. L $\lor$ (M ≡ ∼N) 3. ∼M -Which of the following propositions is derivable from the given premises using the rules available through section 3.4 (MP, MT, DS, HS, Add, Conj, Simp, CD, DM, Dist, Assoc, Com, DN, Cont, Impl, Equiv, Exp, Taut)?

1. (F • ∼ G) ⊃ H 2. J $\lor$ F 3. ∼G • ∼I 4. ∼J / H $\lor$ I -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 derivable from the given premises using the rules available through section 3.2 (MP, MT, DS, HS, Add, Conj, Simp, CD)?

Introducing Logic

Propositional Logic: Syntax and Semantic

Monadic Predicate Logic

Full First-Order Logic

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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. -[(T ⊃ W) • (X ⊃ W)] ⊃ [(T ∨ \lor ∨ X) ⊃ W]

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. (F • ∼ G) ⊃ H 2. J ∨ \lor ∨ F 3. ∼G • ∼I 4. ∼J / H ∨ \lor ∨ I

1. (P ∨ \lor ∨ Q) ∨ \lor ∨ R 2. ∼(S ∨ \lor ∨ Q) -Which of the following propositions is derivable from the given premises using the rules available through 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 -Which of the following propositions is derivable from the given premises using the rules available through section 3.4 (MP, MT, DS, HS, Add, Conj, Simp, CD, DM, Dist, Assoc, Com, DN, Cont, Impl, Equiv, Exp, Taut)?

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. ∼(I ∨ \lor ∨ J) 2. J ⊃ (K ⊃ L) 3. K ≡ ∼L / L

derive the conclusions of each of the following arguments using the rules of inference from section 3.1 (MP, MT, DS, HS). -1. ?J ? K 2. K ? (L ? M) 3. J ? M 4. ?M / ?L

1. G ⊃ H 2. G ⊃ I -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?

1. (A ⊃ C) ⊃ (D ⊃ E) 2. A ⊃ B 3. B ⊃ C -Which of the following propositions is an immediate (one-step) consequence in PL of the given premises?

[F ⊃ (G ∨ \lor ∨ H)] ⊃ [∼G ⊃ (F ⊃ H)] Which of the following propositions is a proper assumption for conditional proof to prove that the above wff is a logical truth of PL?

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. I • (J ∨ \lor ∨ H) 2. I ⊃ ∼J 3. H ≡ (K ∨ \lor ∨ I) / K

1. J ⊃ K 2. ∼J ∨ \lor ∨ L 3. (K • L) ≡ M -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. J ∨ \lor ∨ (M ∨ \lor ∨ L) 2) (∼J ⊃ M) ⊃ K 3) K ⊃ N 4) ∼J • ∼L / N

1. N ⊃ ∼O 2. P ⊃ ∼Q 3. (N ∨ \lor ∨ P) ∨ \lor ∨ R 4. ∼R -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)?

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 ∨ O 2. Q ⊃ ∼O / ∼Q ∨ \lor ∨ P

1. L ⊃ M 2. L ∨ \lor ∨ (M ≡ ∼N) 3. ∼M -Which of the following propositions is derivable from the given premises using the rules available through section 3.4 (MP, MT, DS, HS, Add, Conj, Simp, CD, DM, Dist, Assoc, Com, DN, Cont, Impl, Equiv, Exp, Taut)?

1. (F • ∼ G) ⊃ H 2. J ∨ \lor ∨ F 3. ∼G • ∼I 4. ∼J / H ∨ \lor ∨ I -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 derivable from the given premises using the rules available through section 3.2 (MP, MT, DS, HS, Add, Conj, Simp, CD)?

Introducing Logic

Propositional Logic: Syntax and Semantic

Monadic Predicate Logic

Full First-Order Logic

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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. -[(T ⊃ W) • (X ⊃ W)] ⊃ [(T $\lor$ X) ⊃ W]

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. (F • ∼ G) ⊃ H 2. J $\lor$ F 3. ∼G • ∼I 4. ∼J / H $\lor$ I

1. (P $\lor$ Q) $\lor$ R 2. ∼(S $\lor$ Q) -Which of the following propositions is derivable from the given premises using the rules available through section 3.4 (MP, MT, DS, HS, Add, Conj, Simp, CD, DM, Dist, Assoc, Com, DN, Cont, Impl, Equiv, Exp, Taut)?

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. ∼(I $\lor$ J) 2. J ⊃ (K ⊃ L) 3. K ≡ ∼L / L

[F ⊃ (G $\lor$ H)] ⊃ [∼G ⊃ (F ⊃ H)] Which of the following propositions is a proper assumption for conditional proof to prove that the above wff is a logical truth of PL?

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. I • (J $\lor$ H) 2. I ⊃ ∼J 3. H ≡ (K $\lor$ I) / K

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

1. N ⊃ ∼O 2. P ⊃ ∼Q 3. (N $\lor$ P) $\lor$ R 4. ∼R -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)?

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 $\lor$ O 2. Q ⊃ ∼O / ∼Q $\lor$ P

1. L ⊃ M 2. L $\lor$ (M ≡ ∼N) 3. ∼M -Which of the following propositions is derivable from the given premises using the rules available through section 3.4 (MP, MT, DS, HS, Add, Conj, Simp, CD, DM, Dist, Assoc, Com, DN, Cont, Impl, Equiv, Exp, Taut)?

1. (F • ∼ G) ⊃ H 2. J $\lor$ F 3. ∼G • ∼I 4. ∼J / H $\lor$ I -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 derivable from the given premises using the rules available through section 3.2 (MP, MT, DS, HS, Add, Conj, Simp, CD)?