Question 1

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

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Question 2

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. (G • I) ⊃ H
2. (I ⊃ H) ⊃ F / G ⊃ F

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Question 3

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 ⊃ ∼B
2. A $ \lor $ (B ≡ ∼C)
3. B / ∼C

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Question 4

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

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Question 5

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. L ⊃ M
2. L $ \lor $ (M ≡ ∼N)
3. ∼M / N

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Question 6

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 ⊃ (B ⊃ C)
2. ∼C $ \lor $ (D • E)
3. ∼(D $ \lor $ F) / ∼A $ \lor $ ∼B

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Question 7

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 8

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 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.

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Question 9

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. (P ⊃ Q) ⊃ R
2. ∼(S ⊃ R) / S • ∼Q

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Question 10

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. P ≡ Q
2. ∼Q / P ⊃ R

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Question 11

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

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Question 12

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. (P $ \lor $ Q) ⊃ R
2. R ⊃ ∼Q / ∼Q

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Question 13

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

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Question 14

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

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Question 15

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. M ⊃ J
2. M ⊃ (J ⊃ K)
3. J ⊃ (K ⊃ L) / M ⊃ L

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Question 16

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

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Question 17

translate the given paragraphs into arguments written in PL. Then, derive their conclusions 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).
-If a river is constantly moving and sense experience is veridical, then everything is in flux. If sense experience is veridical, but not our only means of knowledge, then not everything is in flux. So, if a river is constantly moving and sense experience is veridical, then the senses are our only means of knowledge.

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Question 18

derive the conclusions of each of the following arguments using any of the twenty-five rules of PL.
-1. ?A ? B
2. A • ?C / ?(B $ \lor $ C)

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Question 19

derive the conclusions of each of the following arguments using any of the twenty-five rules of PL.
-1. D • ?E / ?D ? E

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Question 20

derive the conclusions of each of the following arguments using any of the twenty-five rules of PL.
-1. (F $ \lor $ G) ? H
2. H • ?G
3. F ? I / I

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Quiz 3: Inference in Propositional Logic

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

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. (G • I) ⊃ H 2. (I ⊃ H) ⊃ F / G ⊃ F

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 ⊃ ∼B 2. A $\lor$ (B ≡ ∼C) 3. B / ∼C

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

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. L ⊃ M 2. L $\lor$ (M ≡ ∼N) 3. ∼M / N

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 ⊃ (B ⊃ C) 2. ∼C $\lor$ (D • E) 3. ∼(D $\lor$ F) / ∼A $\lor$ ∼B

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. (P ⊃ Q) ⊃ R 2. ∼(S ⊃ R) / S • ∼Q

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. P ≡ Q 2. ∼Q / P ⊃ R

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. A ⊃ B 2. B ⊃ (C ⊃ D) 3. A • C 4. ∼D / E

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. (P $\lor$ Q) ⊃ R 2. R ⊃ ∼Q / ∼Q

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

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

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. M ⊃ J 2. M ⊃ (J ⊃ K) 3. J ⊃ (K ⊃ L) / M ⊃ L

derive the conclusions of each of the following arguments using any of the twenty-five rules of PL. -1. ?A ? B 2. A • ?C / ?(B $\lor$ C)

derive the conclusions of each of the following arguments using any of the twenty-five rules of PL. -1. D • ?E / ?D ? E

derive the conclusions of each of the following arguments using any of the twenty-five rules of PL. -1. (F $\lor$ G) ? H 2. H • ?G 3. F ? I / I

Quiz 3: Inference in Propositional Logic

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

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. (G • I) ⊃ H 2. (I ⊃ H) ⊃ F / G ⊃ F

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 ⊃ ∼B 2. A ∨ \lor ∨ (B ≡ ∼C) 3. B / ∼C

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

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. L ⊃ M 2. L ∨ \lor ∨ (M ≡ ∼N) 3. ∼M / N

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 ⊃ (B ⊃ C) 2. ∼C ∨ \lor ∨ (D • E) 3. ∼(D ∨ \lor ∨ F) / ∼A ∨ \lor ∨ ∼B

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. (P ⊃ Q) ⊃ R 2. ∼(S ⊃ R) / S • ∼Q

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. P ≡ Q 2. ∼Q / P ⊃ R

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. A ⊃ B 2. B ⊃ (C ⊃ D) 3. A • C 4. ∼D / E

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. (P ∨ \lor ∨ Q) ⊃ R 2. R ⊃ ∼Q / ∼Q

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

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

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. M ⊃ J 2. M ⊃ (J ⊃ K) 3. J ⊃ (K ⊃ L) / M ⊃ L

derive the conclusions of each of the following arguments using any of the twenty-five rules of PL. -1. ?A ? B 2. A • ?C / ?(B ∨ \lor ∨ C)

derive the conclusions of each of the following arguments using any of the twenty-five rules of PL. -1. D • ?E / ?D ? E

derive the conclusions of each of the following arguments using any of the twenty-five rules of PL. -1. (F ∨ \lor ∨ G) ? H 2. H • ?G 3. F ? I / I

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

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 ⊃ ∼B 2. A $\lor$ (B ≡ ∼C) 3. B / ∼C

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. L ⊃ M 2. L $\lor$ (M ≡ ∼N) 3. ∼M / N

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 ⊃ (B ⊃ C) 2. ∼C $\lor$ (D • E) 3. ∼(D $\lor$ F) / ∼A $\lor$ ∼B

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. (P $\lor$ Q) ⊃ R 2. R ⊃ ∼Q / ∼Q

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

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

derive the conclusions of each of the following arguments using any of the twenty-five rules of PL. -1. ?A ? B 2. A • ?C / ?(B $\lor$ C)

derive the conclusions of each of the following arguments using any of the twenty-five rules of PL. -1. (F $\lor$ G) ? H 2. H • ?G 3. F ? I / I