Deck 3: Inference in Propositional Logic

Question 1

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

A) A
B) B
C) C
D) ∼A
E) ∼C

Answer 1

D

Question 2

1. A ⊃ B
2. ∼B
3. ∼A ⊃ ∼C
-Which of the following propositions is derivable from the given premises using the rules of section 3.1 (MP, MT, DS, HS)?

A) A
B) B
C) C
D) ∼C

Answer 2

D

Question 3

1. T ⊃ S
2. S ⊃ R
3. T
-Which of the following propositions is an immediate (one-step) consequence in PL of the given premises?

A) R
B) S
C) ∼S
D) ∼T

Answer 3

B

Question 4

1. T ⊃ S
2. S ⊃ R
3. T
-Which of the following propositions is derivable from the given premises using the rules of section 3.1 (MP, MT, DS, HS)?

A) R
B) ∼R
C) ∼S
D) ∼T

Question 5

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

A) Q ⊃ R
B) ∼(Q ⊃ R)
C) Q ⊃ S
D) Q ⊃ T
E) Q ⊃ (S • T)

Question 6

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

A) Q
B) R
C) S
D) T
E) Q ⊃ (S • T)

Question 7

1. P ⊃ [Q ⊃ (P ⊃ R)]
2. P
3. Q
-Which of the following propositions is an immediate (one-step) consequence in PL of the given premises?

A) P ⊃ R
B) P ⊃ Q
C) Q ⊃ (P ⊃ Q)
D) Q ⊃ (P ⊃ R)
E) None of the above

Question 8

1. P ⊃ [Q ⊃ (P ⊃ R)]
2. P
3. Q
-Which of the following propositions is derivable from the given premises using the rules of section 3.1 (MP, MT, DS, HS)?

A) ∼P
B) R ⊃ P
C) R
D) ∼R
E) Q ⊃ R

Question 9

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

A) R
B) ∼R
C) P ⊃ Q
D) Q
E) ∼S

Question 10

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)?

A) ∼R
B) P ⊃ R
C) ∼Q
D) ∼S
E) ∼P

Question 11

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?

A) N
B) ∼N
C) P • ∼R
D) Q
E) ∼Q

Question 12

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

A) N
B) ∼(P • ∼R)
C) Q
D) ∼P • ∼∼R
E) O

Question 13

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?

A) ∼J
B) J
C) ∼(K ⊃ L)
D) K
E) L

Question 14

1. ∼J ⊃ K
2. K ⊃ (L ⊃ M)
3. J ⊃ M
4. ∼M
-Which of the following propositions is derivable from the given premises using the rules of section 3.1 (MP, MT, DS, HS)?

A) ∼K
B) J
C) ∼M ⊃ L
D) ∼L
E) L

Question 15

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 is the best translation into PL of this argument?

A) Q $\lor$ R Q ⊃ S
∼S / R
B) Q $\lor$ R S ⊃ Q
∼S / R
C) Q $\lor$ R Q ≡ S
∼A / R
D) Q $\lor$ R S ⊃ Q
∼A / R
E) Q $\lor$ R Q ⊃ S
∼S / Q

Question 16

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?

A) Q
B) ∼Q
C) S ⊃ Q
D) ∼(Q ⊃ S)
E) ∼(Q $\lor$ R)

Question 17

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?

A) MP
B) MT
C) HS
D) DS

Question 18

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 is the best translation into PL of this argument?

A) (O • E) $\lor$ (I • M)
∼(O • E)
∼I / M
B) (O • E) $\lor$ (I • M)
∼(O $\lor$ E)
∼I / M
C) (O $\lor$ E) $\lor$ (I $\lor$ M)
∼(O $\lor$ E)
∼I / M
D) (O $\lor$ E) $\lor$ (I $\lor$ M)
∼(O • E)
∼I / M
E) (O $\lor$ E) • (I $\lor$ M)
∼(O $\lor$ E)
∼I / M

Question 19

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?

A) I
B) O $\lor$ E
C) I $\lor$ M
D) ∼(I $\lor$ M)
E) ∼M

Question 20

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

A) MP
B) MT
C) HS
D) DS

Question 21

1. (F $\lor$ G) ⊃ H
2. F • E
-Which of the following propositions is an immediate (one-step) consequence in PL of the given premises?

A) F $\lor$ G
B) H
C) F
D) G
E) E

Question 22

1. (F $\lor$ G) ⊃ H
2. F • E
-Which of the following propositions is not derivable from the given premises using the rules available through section 3.2 (MP, MT, DS, HS, Add, Conj, Simp, CD)?

A) F
B) F $\lor$ G
C) F $\lor$ ∼G
D) ∼G
E) H

Question 23

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

A) W
B) ∼W
C) Y
D) Y ⊃ Z
E) Z ⊃ W

Question 24

1. ∼W • ∼X
2. Y ⊃ W
3. ∼Y ⊃ Z
-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)?

A) Z $\lor$ X
B) Z • X
C) Y • ∼X
D) Y $\lor$ ∼X
E) ∼Z

Question 25

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?

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

Question 26

1. J ⊃ (K ⊃ L)
2. M ⊃ K
3. M ⊃ J
4. M • K
-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)?

A) J
B) K
C) L
D) All of the above
E) Options A and B, but not option C

Question 27

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

A) R
B) S
C) P ⊃ ∼R
D) ∼R
E) P

Question 28

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

A) (P • Q) • ∼R
B) (∼P • ∼∼Q) • ∼R
C) (∼P • ∼∼S) • ∼R
D) (P • ∼Q) • ∼R
E) (∼P • Q) • R

Question 29

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?

A) ∼G
B) I ⊃ L
C) H ⊃ (I ⊃ J)
D) All of the above
E) Options A and B, but not option C

Question 30

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)?

A) H $\lor$ L
B) G $\lor$ L
C) J $\lor$ L
D) K $\lor$ J
E) G $\lor$ K

Question 31

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

A) A
B) B
C) ∼E
D) B ⊃ A
E) E

Question 32

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)?

A) ∼A
B) B
C) ∼B
D) D ⊃ C
E) A ⊃ E

Question 33

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

A) ∼(B $\lor$ C)
B) B
C) C
D) ∼C
E) B $\lor$ C

Question 34

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)?

A) A
B) B
C) C
D) D
E) E

Question 35

Mica goes swimming only if Nicole lifeguards. Pedro is free on the condition that Ona goes to the beach. Mica goes swimming unless Ona goes to the beach. Nicole doesn't lifeguard. So, either Pedro is free or Mica goes swimming.
-Which of the following is the best translation into PL of this argument?

A) N ⊃ M P ⊃ O
M $\lor$ O
∼N / P $\lor$ M
B) N ⊃ M O ⊃ P
M $\lor$ O
∼N / P $\lor$ M
C) M ⊃ N P ⊃ O
M $\lor$ O
∼N / P $\lor$ M
D) M ⊃ N
O ⊃ P
M $\lor$ O
∼N / P $\lor$ M
E) M ≡ N P ⊃ O
M $\lor$ O
∼N / P $\lor$ M

Question 36

Mica goes swimming only if Nicole lifeguards. Pedro is free on the condition that Ona goes to the beach. Mica goes swimming unless Ona goes to the beach. Nicole doesn't lifeguard. So, either Pedro is free or Mica goes swimming.
-Which of the following propositions is an immediate (one-step) consequence in PL of the given premises?

A) M
B) ∼M
C) N
D) O
E) ∼O

Question 37

Mica goes swimming only if Nicole lifeguards. Pedro is free on the condition that Ona goes to the beach. Mica goes swimming unless Ona goes to the beach. Nicole doesn't lifeguard. So, either Pedro is free or Mica goes swimming.
-Working backward from the conclusion of this argument, which of the following is the most likely justification of the last step of the derivation?

A) MP
B) MT
C) HS
D) Conj
E) Add

Question 38

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

A) R • (∼D ⊃ F) D ⊃ I
∼I
R / F
B) (R • ∼D) ⊃ F D ⊃ F
∼I
N / F
C) (R • ∼D) ⊃ F D ⊃ I
∼I
R / F
D) (R • ∼D) ⊃ F
D ⊃ F
∼F
R / F
E) (R • D) ⊃ F D ⊃ I
∼F
R / F

Question 39

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

A) F
B) ∼F
C) I
D) D
E) ∼D

Question 40

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

A) MP
B) MT
C) DS
D) Add
E) Simp

Question 41

1. ∼E ⊃ F
2. G • ∼E
-Which of the following propositions is an immediate (one-step) consequence in PL of the given premises?

A) F ⊃ ∼E
B) ∼(G • ∼E)
C) F
D) ∼E
E) ∼E • G

Question 42

1. ∼E ⊃ F
2. G • ∼E
-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)?

A) E
B) F
C) ∼G
D) ∼E ⊃ ∼F
E) E $\lor$ ∼F

Question 43

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

A) C $\lor$ D
B) (E $\lor$ C) $\lor$ D
C) ∼[(C $\lor$ E) $\lor$ D]
D) ∼∼E
E) D

Question 44

1. (C $\lor$ E) $\lor$ D
2. ∼E
-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)?

A) C $\lor$ D
B) ∼C $\lor$ D
C) C
D) D
E) ∼C

Question 45

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

A) N
B) N $\lor$ P
C) (R $\lor$ N) $\lor$ P
D) R $\lor$ (N $\lor$ P)
E) ∼∼R

Question 46

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)?

A) N • P
B) ∼N • ∼P
C) ∼(N • P)
D) ∼O • ∼Q
E) ∼(O • Q)

Question 47

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?

A) ∼C
B) ∼(D $\lor$ E)
C) ∼C $\lor$ ∼(D $\lor$ E)
D) ∼C • (∼D $\lor$ ∼E)
E) ∼C • ∼(D $\lor$ E)

Question 48

1. F ⊃ (C $\lor$ D)
2. ∼[C $\lor$ (D $\lor$ E)]
-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)?

A) F
B) ∼F
C) C
D) D
E) E

Question 49

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

A) D • C
B) ∼F
C) ∼C ⊃ (A $\lor$ B)
D) ∼E
E) E

Question 50

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

A) ∼A
B) C • F
C) C
D) ∼D
E) D • F

Question 51

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

A) J $\lor$ ∼(H $\lor$ I)
B) H
C) H • K
D) J
E) G

Question 52

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

A) J • K
B) J • I
C) G • K
D) G ⊃ (H $\lor$ I)
E) ∼H • ∼I

Question 53

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

A) J $\lor$ H
B) J $\lor$ K
C) ∼[G • (H • I)]
D) G $\lor$ (H $\lor$ I)
E) (∼H • ∼I) • ∼G

Question 54

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

A) L $\lor$ M
B) J $\lor$ H
C) G $\lor$ I
D) H $\lor$ I
E) H $\lor$ K

Question 55

After-school activities running late entails that the buses will run late. The buses running late is a sufficient condition for either Carlos and Deandra getting home late or Edna missing dinner. Either after-school activities run late but Carlos doesn't get home late, or after-school activities run late but Deandra doesn't get home late. So, Edna misses dinner.
-Which of the following is the best translation into PL of this argument?

A) A ⊃ B B ⊃ [(C • D) $\lor$ E]
(A $\lor$ ∼C) $\lor$ (A $\lor$ ∼D) / E
B) A ⊃ B B ⊃ [(C • D) $\lor$ E]
(A • ∼C) $\lor$ (A • ∼D) / E
C) A ⊃ B [(C • D) $\lor$ E] ⊃ B
(A • ∼C) $\lor$ (A • ∼D) / E
D) A ⊃ B [(C • D) $\lor$ E] ⊃ B
(A $\lor$ ∼C) $\lor$ (A $\lor$ ∼D) / E
E) A ⊃ B [(C • D) $\lor$ E] ⊃ B
(A $\lor$ ∼C) • (A $\lor$ ∼D) / E

Question 56

After-school activities running late entails that the buses will run late. The buses running late is a sufficient condition for either Carlos and Deandra getting home late or Edna missing dinner. Either after-school activities run late but Carlos doesn't get home late, or after-school activities run late but Deandra doesn't get home late. So, Edna misses dinner.
-Which of the following propositions is an immediate (one-step) consequence in PL of the given premises?

A) A • (∼C $\lor$ ∼D)
B) A • (∼C • ∼D)
C) A $\lor$ (∼C $\lor$ ∼D)
D) A $\lor$ (∼C • ∼D)
E) A ⊃ [(C • D) • E]

Question 57

After-school activities running late entails that the buses will run late. The buses running late is a sufficient condition for either Carlos and Deandra getting home late or Edna missing dinner. Either after-school activities run late but Carlos doesn't get home late, or after-school activities run late but Deandra doesn't get home late. So, Edna misses dinner.
-Working backward from the conclusion of this argument, which of the following is the most likely justification of the last step of the derivation?

A) MP
B) Simp
C) DN
D) DS
E) HS

Question 58

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 is the best translation into PL of this argument?

A) O ⊃ ∼D T ⊃ C
D / ∼T
B) O ⊃ ∼D C ⊃ T
D / ∼T
C) (O • C) ⊃ ∼D T ⊃ C
D / ∼T
D) (O $\lor$ C) ⊃ ∼D T ⊃ C
D / ∼T
E) (O $\lor$ C) ⊃ ∼D T ⊃ O
D / ∼T

Question 59

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?

A) ∼(O $\lor$ C)
B) C
C) ∼∼D
D) ∼∼T
E) ∼T

Question 60

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

A) Com
B) DS
C) MT
D) MP
E) CD

Question 61

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

A) ∼S $\lor$ ∼Q
B) ∼S • ∼Q
C) ∼Q • ∼S
D) (P $\lor$ R) $\lor$ Q
E) Q $\lor$ (P $\lor$ R)

Question 62

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)?

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

Question 63

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

A) ∼O ⊃ ∼Q
B) ∼O ⊃ Q
C) O ⊃ Q
D) ∼∼O ⊃ ∼Q
E) ∼∼O ⊃ ∼∼Q

Question 64

1. P $\lor$ O
2. Q ⊃ ∼O
-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)?

A) O
B) P
C) Q
D) O ⊃ P
E) ∼Q $\lor$ P

Question 65

1. (G • I) ⊃ H
2. (I ⊃ H) ⊃ F
-Which of the following propositions is an immediate (one-step) consequence in PL of the given premises?

A) G ⊃ (I ⊃ H)
B) (G ⊃ I) ⊃ H
C) (I • H) ⊃ F
D) I ⊃ (H ⊃ F)
E) I ⊃ (H • F)

Question 66

1. (G • I) ⊃ H
2. (I ⊃ H) ⊃ F
-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)?

A) G ⊃ I
B) G ⊃ H
C) I ⊃ H
D) I ⊃ F
E) G ⊃ F

Question 67

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?

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

Question 68

1. A ⊃ ∼B
2. A $\lor$ (B ≡ ∼C)
3. B
-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)?

A) A
B) ∼B
C) ∼C
D) All of the above
E) None of the above

Question 69

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?

A) B ⊃ A
B) ∼A ⊃ ∼B
C) A ⊃ C
D) C ⊃ B
E) ∼C ⊃ B

Question 70

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)?

A) C ⊃ A
B) ∼C ⊃ A
C) E ⊃ D
D) ∼D ⊃ ∼E
E) ∼E ⊃ ∼D

Question 71

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?

A) L
B) ∼L
C) M
D) ∼N
E) None of the above

Question 72

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)?

A) ∼M ≡ ∼N
B) ∼M ⊃ ∼N
C) N ⊃ M
D) N
E) L

Question 73

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

A) (A • B) ⊃ C
B) C ⊃ (D • E)
C) ∼D • ∼F
D) Options A, B, and C
E) Options B and C, but not A

Question 74

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

A) ∼A $\lor$ ∼B
B) ∼(A • B)
C) A ⊃ ∼B
D) B ⊃ ∼A
E) All of the above

Question 75

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

A) M ⊃ A ∼R ⊃ M
A $\lor$ ∼R / M
B) A ⊃ M ∼R ⊃ M
A $\lor$ ∼R / M
C) A ⊃ M R ⊃ M
A ⊃ ∼R / M
D) A ⊃ M R ⊃ M
A $\lor$ ∼R / M
E) M ⊃ A M ⊃ ∼R
A $\lor$ ∼R / M

Question 76

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

A) A $\lor$ M
B) ∼R $\lor$ M
C) A ⊃ ∼R
D) M $\lor$ M
E) None of the above

Question 77

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?

A) MT
B) HS
C) Impl
D) DS
E) Taut

Question 78

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

A) N ⊃ M S ⊃ R
∼N ⊃ M
V ⊃ (∼M • R) / ∼V
B) N ⊃ M S ⊃ R
N ⊃ M
V ⊃ (∼M • R) / ∼V
C) N ⊃ M S ⊃ ∼R
∼N ⊃ S
V ⊃ (∼M • R) / ∼V
D) N ⊃ M S ⊃ ∼R
∼N ⊃ S
V ⊃ ∼M / ∼V
E) N ⊃ M M ⊃ ∼R
∼N ⊃ M
(V ⊃ ∼M) • R / ∼V

Question 79

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

A) N $\lor$ S
B) ∼∼N $\lor$ S
C) S ⊃ ∼N
D) M ⊃ N
E) N $\lor$ M

Question 80

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?

A) Cont
B) MT
C) Taut
D) DS
E) CD