Question 1

Given the following premises:
1) (K • ∼T)  ∨ (K • ∼H) 
2) ∼M ⊃ (K • ∼H) 
3) ∼(K • ∼H)

Accepted Answer

A)  ∼K ∨ H 3, DM
B)  K • ∼T 1, 3, DS
C)  K • (∼T ∨ ∼H)  1, Dist
D)  M 2, 3, MT
E)  (∼M • K)  ⊃ ∼H 2, ExpF) None of the above
G) D) and E)

Question 2

Given the following premises:
1) (J • ∼N)  ∨ T
2) ∼(J • ∼N) 
3) ∼T

Accepted Answer

A)  T 1, 2, DS
B)  ∼J ∨ N 2, DM
C)  J • ∼N 1, 3, DS
D)  J • (∼N ∨ T)  1, Assoc
E)  ∼J 2, SimpF) A) and B)
G) A) and C)

Question 3

Given the following premises:
1) D ⊃ (∼A ∨ ∼A) 
2) ∼A ⊃ (R • M) 
3) ∼R • ∼M

Accepted Answer

A)  D ⊃ ∼A 1, Taut
B)  D ⊃ A 1, DN
C)  D ⊃ (R • M)  1, 2, HS
D)  ∼∼A 2, 3, MT
E)  ∼(R • M)  3, DMF) A) and E)
G) A) and B)

Question 4

Given the following premises:
1) (L ⊃ M)  • (F ⊃ J) 
2) M ⊃ ∼(F ∨ L) 
3) F ∨ L

Accepted Answer

A)  L ⊃ ∼(F ∨ L)  1, 2, HS
B)  M ∨ J 1, 3, CD
C)  L ⊃ M 1, Simp
D)  ∼M 2, 3, MT
E)  M ⊃ (∼F ∨ ∼L)  2, DMF) C) and D)
G) B) and E)

Question 5

Given the following premises:
1) F ∨ S
2) ∼S
3) (S ⊃ W)  • (F ⊃ N)

Accepted Answer

A)  F 1, 2, DS
B)  S ⊃ W 3, Simp
C)  ∼F ⊃ S 1, Impl
D)  F ⊃ N 3, Simp
E)  W ∨ N 1, 3, CDF) All of the above
G) A) and E)

Question 6

Given the following premises:
1) ∼(∼H • J) 
2) K ∨ (∼H • J) 
3) (M ∨ M)  ⊃ (∼H • J)

Accepted Answer

A)  (K ∨ ∼H)  • (K ∨ J)  2, Dist
B)  ∼K ⊃ (∼H • J)  2, Impl
C)  K 1, 2, DS
D)  H ∨ ∼J 1, DM
E)  ∼M 1, 3, MTF) A) and D)
G) A) and B)

Question 7

Given the following premises:
1) H ∨ M
2) E ⊃ ∼(H ∨ M) 
3) (H ⊃ D)  • (M ⊃ O)

Accepted Answer

A)  ∼H ⊃ M 1, Impl
B)  ∼E 1, 2, MT
C)  H 1, Simp
D)  M ⊃ O 3, Simp
E)  D ∨ O 1, 3, CDF) B) and C)
G) B) and D)

Question 8

Use conditional proof:
1.S ⊃ (B ⊃ T)
2.N ⊃ (T ⊃ ∼B)
/ (S • N) ⊃ ∼B

Accepted Answer

To prove the argument using conditional ...

Question 9

Given the following premises:
1) T ∨ S
2) A ⊃ T
3) A • (∼T • S)

Accepted Answer

A)  ∼T 3, Simp
B)  (A • ∼T)  • S 3, Assoc
C)  T 2, 3, MP
D)  T ⊃ A 2, Com
E)  S 1, 3, DSF) A) and B)
G) A) and C)

Question 10

Use natural deduction to prove the following logical truth:
[(P ∨ Q) ⊃ (R • T)] ⊃ (P ⊃ R)

Accepted Answer

To prove the logical truth of `[(P ∨ Q) ...

Question 11

Given the following premises:
1) ∼E ⊃ P
2) ∼P
3) ∼(P ∨ ∼H)

Accepted Answer

A)  ∼H 2, 3, DS
B)  ∼P • ∼(P ∨ ∼H)  2, 3, Conj
C)  ∼P • H 3, DM
D)  E 1, 2, MT
E)  ∼P ⊃ E 1, TransF) A) and B)
G) B) and E)

Question 12

Given the following premises:
1) N ∨ C
2) (N ∨ C)  ⊃ (F ⊃ C) 
3) ∼C

Accepted Answer

A)  F ⊃ C 1, 2, MP
B)  N 1, 3, DS
C)  ∼F 2, 3, MT
D)  ∼N 1, 3, MT
E)  ∼C • R 3, AddF) None of the above
G) A) and E)

Question 13

Given the following premises:
1) ∼(G • F) 
2) ∼F ⊃ H
3) (G ⊃ ∼F)  • (∼F ⊃ G)

Accepted Answer

A)  ∼F ⊃ G 3, Simp
B)  G ⊃ H 2, 3, HS
C)  F ∨ H 2, Impl
D)  G ≡ ∼F 3, Equiv
E)  ∼G 1, SimpF) B) and C)
G) A) and B)

Question 14

Given the following premises:
1) N ⊃ ∼(S ∨ K) 
2) S ∨ K
3) S ⊃ (R • Q)

Accepted Answer

A)  S 2, Simp
B)  (S ∨ K)  ∨ N 2, Add
C)  ∼S ⊃ K 2, Impl
D)  ∼N 1, 2, MT
E)  (S ⊃ R)  ⊃ Q 3, ExpF) A) and B)
G) C) and D)

Question 15

Given the following premises:
1) ∼∼N
2) K ⊃ ∼N
3) ∼N ∨ (K • S)

Accepted Answer

A)  (∼N ∨ K)  • S 3, Assoc
B)  K 1, 2, MT
C)  N ⊃ ∼K 2, Trans
D)  K • S 1, 3, DS
E)  (∼N • K)  ∨ (∼N • S)  3, DistF) A) and D)
G) B) and E)

Question 16

Use an ordinary proof (not conditional or indirect proof):
1.F ⊃ (J ∨ ∼F)
2.J ⊃ (L ∨ ∼J)
/ F ⊃ L

Accepted Answer

To prove F ⊃ L using an ordinary proof w...

Question 17

Use an ordinary proof (not conditional or indirect proof):
1.M ⊃ (R • E)
2.(E ∨ H) ⊃ G
/ M ⊃ G

Accepted Answer

To prove that M ⊃ G using an ordinary pr...

Question 18

Given the following premises:
1) F ⊃ J
2) A ⊃ (F • J) 
3) A • (Q ∨ N)

Accepted Answer

A)  J ⊃ F 1, Com
B)  A • (N ∨ Q)  3, Com
C)  A ⊃ J 1, 2, HS
D)  (A ⊃ F)  • (A ⊃ J)  2, Dist
E)  (A • Q)  ∨ N 3, AssocF) D) and E)
G) C) and D)

Question 19

Use an ordinary proof (not conditional or indirect proof):
1.∼N ⊃ (∼R ⊃ C)
2.R ⊃ N
3.∼C
/ N

Accepted Answer

To prove that N is true using an ordinar...

Question 20

Given the following premises:
1) B
2) ∼R ⊃ K
3) B ⊃ (K ⊃ E)

Accepted Answer

A)  (B ⊃ K)  ⊃ E 3, Assoc
B)  ∼R ⊃ E 2, 3, HS
C)  R ∨ K 2, Impl
D)  K ⊃ E 1, 3, MP
E)  B • N 1, AddF) B) and D)
G) A) and B)

Exam 7: Natural Deduction in Propositional Logic

Given the following premises: 1) ∼(∼H • J) 2) K ∨ (∼H • J) 3) (M ∨ M) ⊃ (∼H • J)

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Use natural deduction to prove the following logical truth: [(P ∨ Q) ⊃ (R • T)] ⊃ (P ⊃ R)

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Given the following premises: 1) (L ⊃ M) • (F ⊃ J) 2) M ⊃ ∼(F ∨ L) 3) F ∨ L

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Use an ordinary proof (not conditional or indirect proof): 1.M ⊃ (R • E) 2.(E ∨ H) ⊃ G / M ⊃ G

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Given the following premises: 1) N ⊃ ∼(S ∨ K) 2) S ∨ K 3) S ⊃ (R • Q)

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Given the following premises: 1) F ⊃ J 2) A ⊃ (F • J) 3) A • (Q ∨ N)

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Given the following premises: 1) (K • ∼T) ∨ (K • ∼H) 2) ∼M ⊃ (K • ∼H) 3) ∼(K • ∼H)

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Use conditional proof: 1.S ⊃ (B ⊃ T) 2.N ⊃ (T ⊃ ∼B) / (S • N) ⊃ ∼B

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Use an ordinary proof (not conditional or indirect proof): 1.∼N ⊃ (∼R ⊃ C) 2.R ⊃ N 3.∼C / N

Correct AnswerAnswered by ExamLex AITo prove that N is true using an ordinar...View AnswerShow Answer

Given the following premises: 1) (J • ∼N) ∨ T 2) ∼(J • ∼N) 3) ∼T

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Given the following premises: 1) N ∨ C 2) (N ∨ C) ⊃ (F ⊃ C) 3) ∼C

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Given the following premises: 1) D ⊃ (∼A ∨ ∼A) 2) ∼A ⊃ (R • M) 3) ∼R • ∼M

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Given the following premises: 1) F ∨ S 2) ∼S 3) (S ⊃ W) • (F ⊃ N)

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Given the following premises: 1) ∼∼N 2) K ⊃ ∼N 3) ∼N ∨ (K • S)

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Given the following premises: 1) H ∨ M 2) E ⊃ ∼(H ∨ M) 3) (H ⊃ D) • (M ⊃ O)

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Given the following premises: 1) B 2) ∼R ⊃ K 3) B ⊃ (K ⊃ E)

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Given the following premises: 1) ∼(G • F) 2) ∼F ⊃ H 3) (G ⊃ ∼F) • (∼F ⊃ G)

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Use an ordinary proof (not conditional or indirect proof): 1.F ⊃ (J ∨ ∼F) 2.J ⊃ (L ∨ ∼J) / F ⊃ L

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Given the following premises: 1) ∼E ⊃ P 2) ∼P 3) ∼(P ∨ ∼H)

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Given the following premises: 1) T ∨ S 2) A ⊃ T 3) A • (∼T • S)

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