Question 1

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

Accepted Answer

A)   [(G • H)  ⊃ I] ⊃ [G ⊃ (H ⊃ I) ]
B)   [(G • H)  ⊃ I] ⊃ (G ⊃ H) 
C)   [(G • H)  ⊃ I] ⊃ G
D)   (G • H)  ⊃ I
E)   G • HF) A) and B)
G) B) and E)

Question 2

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

Accepted Answer

A)   (A • L)   ∨ \lor ∨  (L • G)  E ⊃ ∼L / ∼E
B)   N  ∨ \lor ∨  ∼N E ⊃ L / ∼E
C)   (A  ∨ \lor ∨  L)  • (L  ∨ \lor ∨  G)  E ⊃ ∼L / ∼E
D)   N  ∨ \lor ∨  ∼N E ⊃ ∼L / ∼E
E)   (A • L)   ∨ \lor ∨  (L • G)  E ⊃ L / ∼E F) C) and D)
G) A) and B)

Question 3

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

Accepted Answer

The answer of derive the conclusions of each of the...

Question 4

1. A ⊃ ∼B
2. A  ∨ \lor ∨  (B ≡ ∼C) 
3. B
-Which of the following propositions is an immediate (one-step)  consequence in PL of the given premises?

Accepted Answer

A)   ∼A
B)   ∼∼B
C)   (A  ∨ \lor ∨  
B)   ≡ (A  ∨ \lor ∨  ∼
C)  
D)   Options A, B, and C
E)   Options A and B, but not C F) A) and B)
G) A) and C)

Question 5

1. P ≡ Q
2. ∼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) ?

Accepted Answer

A)   ∼P ⊃∼Q
B)   ∼Q ⊃ ∼P
C)   P ⊃ R
D)   All of the above
E)   Options A and B, but not option CF) A) and E)
G) None of the above

Question 6

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

Accepted Answer

The answer of derive the conclusions of each of the...

Question 7

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

Accepted Answer

A)   Impl
B)   DM
C)   DS
D)   Equiv
E)   ContF) A) and B)
G) A) and C)

Question 8

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

Accepted Answer

A)   A
B)   D
C)   B  ∨ \lor ∨  ∼C
D)   ∼B • ∼E
E)   (B  ∨ \lor ∨  ∼
C)    ∨ \lor ∨  (∼B • ∼
E)   F) B) and D)
G) C) and D)

Question 9

1. (P  ∨ \lor ∨  ∼R)  ⊃ (P ⊃ Q) 
2. P  ∨ \lor ∨  ∼R
3. P
4. Q ⊃ ∼S
-Which of the following propositions is derivable from the given premises using the rules of section 3.1 (MP, MT, DS, HS) ?

Accepted Answer

A)   ∼R
B)   P ⊃ R
C)   ∼Q
D)   ∼S
E)   ∼P F) C) and D)
G) A) and C)

Question 10

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. P ? ?Q
2. ?R $ \lor $ ??Q
3. ?R ? S
4. ?S / (?P • ??Q) • ??R

Accepted Answer

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\text { 1. } \m...

Question 11

(P  ∨ \lor ∨  Q)   ∨ \lor ∨  (∼P • ∼Q) 
-Which of the following propositions is an appropriate assumption for an indirect proof of the given logical truth?

Accepted Answer

A)   (P  ∨ \lor ∨  Q)   ∨ \lor ∨  (∼P • ∼Q) 
B)   ∼[(P  ∨ \lor ∨  Q)   ∨ \lor ∨  (∼P • ∼Q) ]
C)   ∼(P  ∨ \lor ∨  Q) 
D)   P  ∨ \lor ∨  Q
E)   ∼(P  ∨ \lor ∨  Q)   ∨ \lor ∨  ∼(∼P • ∼Q)  F) C) and E)
G) D) and E)

Question 12

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

Accepted Answer

A)   Valid
B)   Invalid. Counterexample when H and I are true and J and K are false
C)   Invalid. Counterexample when I is true and H, J, and K are false
D)   Invalid. Counterexample when H, I, and J are true and K is false
E)   Invalid. Counterexample when J is true, and H, I, and K are false F) A) and B)
G) A) and C)

Question 13

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

Accepted Answer

A)   MT
B)   HS
C)   Impl
D)   DS
E)   TautF) A) and D)
G) B) and C)

Question 14

1. D • ∼E
-Which of the following propositions is derivable from the given premise using any of the twenty-five rules of PL?

Accepted Answer

A)   D ≡ E
B)   ∼D ≡ E
C)   ∼D ≡ ∼E
D)   D ⊃ E
E)   ∼D ⊃ ∼EF) A) and D)
G) A) and C)

Question 15

Explanations are good just in case understanding is increased. Understanding is not increased if, and only if, explanations are empirical deductions. So, explanations are good if, and only if, they are not logical deductions.
-Consider assuming '∼D' 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?

Accepted Answer

A)   ∼U
B)   ∼∼U
C)   ∼D ≡ U
D)   D ≡ ∼U
E)   D ≡ UF) B) and D)
G) A) and D)

Question 16

1. V ≡ (W  ∨ \lor ∨  ∼X) 
2. ∼Y ≡ ∼V
3. (W ⊃ Y)  ⊃ Z
-Which of the following propositions is an immediate (one-step)  consequence in PL of the given premises?

Accepted Answer

A)   ∼(Y ≡ V) 
B)   ∼(∼Y ≡ ∼V) 
C)   Y ≡ ∼V
D)   V ≡ ∼Y
E)   Y ≡ V F) D) and E)
G) A) and E)

Question 17

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

Accepted Answer

A)   J
B)   M ⊃ L
C)   M ⊃ (K ⊃ L) 
D)   All of the above
E)   Options B and C, but not option AF) A) and E)
G) C) and D)

Question 18

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.

Accepted Answer

1.

2.

, Impl
3.

2,

4.

3, Com \[\begin ...

Question 19

1. F ⊃ (C  ∨ \lor ∨  D) 
2. ∼[C  ∨ \lor ∨  (D  ∨ \lor ∨  E) ]
-Which of the following propositions is an immediate (one-step)  consequence in PL of the given premises?

Accepted Answer

A)   ∼C
B)   ∼(D  ∨ \lor ∨  
E)  
C)   ∼C  ∨ \lor ∨  ∼(D  ∨ \lor ∨  
E)  
D)   ∼C • (∼D  ∨ \lor ∨  ∼
E)  
E)   ∼C • ∼(D  ∨ \lor ∨  
E)   F) B) and E)
G) A) and D)

Question 20

1. ∼(K • J) 
2. I  ∨ \lor ∨  (L • J)  / ∼K  ∨ \lor ∨  I
-Which of the following propositions is an appropriate assumption for an indirect proof of the conclusion of the given argument?

Accepted Answer

A)   K
B)   ∼K
C)   ∼(K  ∨ \lor ∨  I) 
D)   ∼(∼K  ∨ \lor ∨  I) 
E)   ∼∼(∼K  ∨ \lor ∨  I)  F) C) and D)
G) A) and D)

Exam 3: Inference in Propositional Logic

1. ∼(K • J) 2. I $\lor$ (L • J) / ∼K $\lor$ I -Which of the following propositions is an appropriate assumption for an indirect proof of the conclusion of the given argument?

Correct Answer
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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. P ? ?Q 2. ?R $\lor$ ??Q 3. ?R ? S 4. ?S / (?P • ??Q) • ??R

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

Correct Answer
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Correct Answer
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Correct Answer
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2. , Impl
3. 2,
4. 3, Com \[\begin ...
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determine whether the argument is valid or invalid. If it is invalid, select a counterexample. -1. I • (J $\lor$ H) 2) I ⊃ ∼J 3) H ≡ (K $\lor$ I) / K

Correct Answer
verified

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

Correct Answer
verified

1. (P $\lor$ ∼R) ⊃ (P ⊃ Q) 2. P $\lor$ ∼R 3. P 4. Q ⊃ ∼S -Which of the following propositions is derivable from the given premises using the rules of section 3.1 (MP, MT, DS, HS) ?

Correct Answer
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(P $\lor$ Q) $\lor$ (∼P • ∼Q) -Which of the following propositions is an appropriate assumption for an indirect proof of the given logical truth?

Correct Answer
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1. V ≡ (W $\lor$ ∼X) 2. ∼Y ≡ ∼V 3. (W ⊃ Y) ⊃ Z -Which of the following propositions is an immediate (one-step) consequence in PL of the given premises?

Correct Answer
verified

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

Correct Answer
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1. D • ∼E -Which of the following propositions is derivable from the given premise using any of the twenty-five rules of PL?

Correct Answer
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1. F ⊃ (C $\lor$ D) 2. ∼[C $\lor$ (D $\lor$ E) ] -Which of the following propositions is an immediate (one-step) consequence in PL of the given premises?

Correct Answer
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1. A ⊃ ∼B 2. A $\lor$ (B ≡ ∼C) 3. B -Which of the following propositions is an immediate (one-step) consequence in PL of the given premises?

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

Correct Answer
verified

Correct Answer
verified

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

Correct Answer
verified

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

Correct Answer
verified

1. P ≡ Q 2. ∼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) ?

Correct Answer
verified

Exam 3: Inference in Propositional Logic

1. ∼(K • J) 2. I ∨ \lor ∨ (L • J) / ∼K ∨ \lor ∨ I -Which of the following propositions is an appropriate assumption for an indirect proof of the conclusion of the given argument?

Correct AnswerverifiedShow Answer

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. P ? ?Q 2. ?R ∨ \lor ∨ ??Q 3. ?R ? S 4. ?S / (?P • ??Q) • ??R

Correct Answerverified\[\begin{array} { l l } \text { 1. } \m...View AnswerShow Answer

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

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Correct Answerverified 1. 2. , Impl3. 2, 4. 3, Com \[\begin ...View AnswerShow Answer

determine whether the argument is valid or invalid. If it is invalid, select a counterexample. -1. I • (J ∨ \lor ∨ H) 2) I ⊃ ∼J 3) H ≡ (K ∨ \lor ∨ I) / K

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

1. (P ∨ \lor ∨ ∼R) ⊃ (P ⊃ Q) 2. P ∨ \lor ∨ ∼R 3. P 4. Q ⊃ ∼S -Which of the following propositions is derivable from the given premises using the rules of section 3.1 (MP, MT, DS, HS) ?

Correct AnswerverifiedShow Answer

(P ∨ \lor ∨ Q) ∨ \lor ∨ (∼P • ∼Q) -Which of the following propositions is an appropriate assumption for an indirect proof of the given logical truth?

Correct AnswerverifiedShow Answer

1. V ≡ (W ∨ \lor ∨ ∼X) 2. ∼Y ≡ ∼V 3. (W ⊃ Y) ⊃ Z -Which of the following propositions is an immediate (one-step) consequence in PL of the given premises?

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

1. D • ∼E -Which of the following propositions is derivable from the given premise using any of the twenty-five rules of PL?

Correct AnswerverifiedShow Answer

1. F ⊃ (C ∨ \lor ∨ D) 2. ∼[C ∨ \lor ∨ (D ∨ \lor ∨ E) ] -Which of the following propositions is an immediate (one-step) consequence in PL of the given premises?

Correct AnswerverifiedShow Answer

1. A ⊃ ∼B 2. A ∨ \lor ∨ (B ≡ ∼C) 3. B -Which of the following propositions is an immediate (one-step) consequence in PL of the given premises?

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Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

1. P ≡ Q 2. ∼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) ?

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1. ∼(K • J) 2. I $\lor$ (L • J) / ∼K $\lor$ I -Which of the following propositions is an appropriate assumption for an indirect proof of the conclusion of the given argument?

Correct Answer
verified

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. P ? ?Q 2. ?R $\lor$ ??Q 3. ?R ? S 4. ?S / (?P • ??Q) • ??R

Correct Answer
verified
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View Answer

Correct Answer
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Correct Answer
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Correct Answer
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1.
2. , Impl
3. 2,
4. 3, Com \[\begin ...
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determine whether the argument is valid or invalid. If it is invalid, select a counterexample. -1. I • (J $\lor$ H) 2) I ⊃ ∼J 3) H ≡ (K $\lor$ I) / K

Correct Answer
verified

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

Correct Answer
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1. (P $\lor$ ∼R) ⊃ (P ⊃ Q) 2. P $\lor$ ∼R 3. P 4. Q ⊃ ∼S -Which of the following propositions is derivable from the given premises using the rules of section 3.1 (MP, MT, DS, HS) ?

Correct Answer
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(P $\lor$ Q) $\lor$ (∼P • ∼Q) -Which of the following propositions is an appropriate assumption for an indirect proof of the given logical truth?

Correct Answer
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1. V ≡ (W $\lor$ ∼X) 2. ∼Y ≡ ∼V 3. (W ⊃ Y) ⊃ Z -Which of the following propositions is an immediate (one-step) consequence in PL of the given premises?

Correct Answer
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Correct Answer
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Correct Answer
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1. F ⊃ (C $\lor$ D) 2. ∼[C $\lor$ (D $\lor$ E) ] -Which of the following propositions is an immediate (one-step) consequence in PL of the given premises?

Correct Answer
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1. A ⊃ ∼B 2. A $\lor$ (B ≡ ∼C) 3. B -Which of the following propositions is an immediate (one-step) consequence in PL of the given premises?

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

Correct Answer
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Correct Answer
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