Question 1

Given the following premises:
1.(C • ∼F) ⊃ E
2.G ∨ (C • ∼F)
3.∼(C • ∼F)

Accepted Answer

A) G ⊃ E 1, 2, HS 
B) C 1, Simp 
C) C ⊃ (∼F ⊃ 
E)  1, Exp 
D) (G ∨ 
C)  • ∼F 2, Assoc 
E) (G ∨ 
C)  • ∼F 2, Assoc . 
A) G ⊃ E 1, 2, HS 
B) C 1, Simp 
C) C ⊃ (∼F ⊃ 
E)  1, Exp 
D) (G ∨ 
C)  • ∼F 2, Assoc 
E) (G ∨ 
C)  • ∼F 2, Assoc .

Question 2

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 3

Use conditional proof:
1.N ⊃ (F • A)
2.B ⊃ (R • F)/ (N ∨ B) ⊃ (A∨ R)

Accepted Answer

To prove the argument using conditional

Question 4

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, Add 
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, Add

Question 5

Given the following premises:
1)Q ⊃ (∼N ∨ ∼N)
2)∼N ⊃ ∼∼P
3)P ⊃ ∼G

Accepted Answer

A) ∼N ⊃ P 2, DN 
B) Q ⊃ ∼∼P 1, 2, HS 
C) N ∨ P 2, Impl 
D) ∼N ⊃ ∼G 2, 3, HS 
E) G ⊃ ∼P 3, Trans 
A) ∼N ⊃ P 2, DN 
B) Q ⊃ ∼∼P 1, 2, HS 
C) N ∨ P 2, Impl 
D) ∼N ⊃ ∼G 2, 3, HS 
E) G ⊃ ∼P 3, Trans

Question 6

Use natural deduction to prove the following logical truth:
[F • (D ⊃ ∼F)] ⊃ (D ⊃ A)

Accepted Answer

To prove the logical truth of the statem

Question 7

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

Accepted Answer

A) S ⊃ B 1, HS 
B) ∼F ∨ B 1, 2, CD 
C) S 2, 3, DS 
D) B 1, 3, MP 
E) ∼S 1, 3, MT 
A) S ⊃ B 1, HS 
B) ∼F ∨ B 1, 2, CD 
C) S 2, 3, DS 
D) B 1, 3, MP 
E) ∼S 1, 3, MT

Question 8

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

Question 9

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

Accepted Answer

A) (P • M) ⊃ ∼R 3, Taut 
B) P 3, Simp 
C) L ⊃ (∼R ∨ ∼R) 2, 3, HS 
D) (L ⊃ P) ∨ (L ⊃ M) 2, Dist 
E) M 1, 2, DS 
A) (P • M) ⊃ ∼R 3, Taut 
B) P 3, Simp 
C) L ⊃ (∼R ∨ ∼R) 2, 3, HS 
D) (L ⊃ P) ∨ (L ⊃ M) 2, Dist 
E) M 1, 2, DS

Question 10

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

Accepted Answer

A) ∼(F • ∼M) 1, 3, MT 
B) ∼L 3, Simp 
C) ∼P 2, 3, MT 
D) ∼L ∨ G 3, DM 
E) L ⊃ P 2, Trans 
A) ∼(F • ∼M) 1, 3, MT 
B) ∼L 3, Simp 
C) ∼P 2, 3, MT 
D) ∼L ∨ G 3, DM 
E) L ⊃ P 2, Trans

Question 11

Given the following premises:
1)(E ⊃ K) ∨ W
2)∼W
3)W ∨ ∼(Q ⊃ E)

Accepted Answer

A) E ⊃ K 1, 2, DS 
B) Q ⊃ K 1, 3, HS 
C) ∼(Q ⊃ 
E)  2, 3, DS 
D) E ⊃ (K ∨ W) 1, Assoc 
E) W ∨ (∼Q ⊃ ∼
E)  3, DM 
A) E ⊃ K 1, 2, DS 
B) Q ⊃ K 1, 3, HS 
C) ∼(Q ⊃ 
E)  2, 3, DS 
D) E ⊃ (K ∨ W) 1, Assoc 
E) W ∨ (∼Q ⊃ ∼
E)  3, DM

Question 12

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

Accepted Answer

A) Q ⊃ (N • ∼H) 2, DM 
B) H ⊃ Q 3, Simp 
C) ∼Q 1, 2, MT 
D) ∼N ⊃ ∼(∼N ∨ H) 2, 3, HS 
E) Q ∨ Q 1, 3, CD 
A) Q ⊃ (N • ∼H) 2, DM 
B) H ⊃ Q 3, Simp 
C) ∼Q 1, 2, MT 
D) ∼N ⊃ ∼(∼N ∨ H) 2, 3, HS 
E) Q ∨ Q 1, 3, CD

Question 13

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

Accepted Answer

A) ∼(C • L) 2, 3, MT 
B) (C ⊃ ∼L) ∨ ∼N 1, Assoc 
C) (C ⊃ ∼N) • (L ⊃ ∼N) 2, Dist 
D) C ⊃ ∼N 2, Simp 
E) C ⊃ ∼(L • N) 1, DM 
A) ∼(C • L) 2, 3, MT 
B) (C ⊃ ∼L) ∨ ∼N 1, Assoc 
C) (C ⊃ ∼N) • (L ⊃ ∼N) 2, Dist 
D) C ⊃ ∼N 2, Simp 
E) C ⊃ ∼(L • N) 1, DM

Question 14

Given the following premises:
1)(S • ∼J) ∨ (∼S • ∼∼J)
2)S ∨ ∼S
3)∼J ⊃ P

Accepted Answer

A) S 2, Taut 
B) ∼J ∨ ∼∼J 1, 2, CD 
C) S ≡ ∼J 1, Equiv 
D) J ∨ P 3, Impl 
E) ∼P ⊃ J 3, Trans 
A) S 2, Taut 
B) ∼J ∨ ∼∼J 1, 2, CD 
C) S ≡ ∼J 1, Equiv 
D) J ∨ P 3, Impl 
E) ∼P ⊃ J 3, Trans

Question 15

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, DM 
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, DM

Question 16

Given the following premises:
1)∼R ≡ ˜R
2)N • ˜T
3)R ⊃ ˜(N • ˜T)

Accepted Answer

A) ∼T 2, Simp 
B) (N • ∼T) ⊃ ∼R 3, Trans 
C) ∼R 2, 3, MT 
D) R ⊃ (∼N ∨ ∼∼T) 3, DM 
E) ∼R 1, Taut 
A) ∼T 2, Simp 
B) (N • ∼T) ⊃ ∼R 3, Trans 
C) ∼R 2, 3, MT 
D) R ⊃ (∼N ∨ ∼∼T) 3, DM 
E) ∼R 1, Taut

Question 17

Use an ordinary proof (not conditional or indirect proof):
1.S ⊃ (K • F)
2.F ⊃ (G • H)/ S ⊃ H

Accepted Answer

To prove that S ⊃ H using an ordinary pr

Question 18

Given the following premises:
1)Q ⊃ (H • L)
2)H ⊃ ∼Q
3)L ⊃ ∼Q

Accepted Answer

A) (Q ⊃ H) ⊃ L 1, Exp 
B) L ⊃ (H • L) 1, 3, HS 
C) Q ⊃ ∼Q 1, 3, HS 
D) H ⊃ L 2, 3, HS 
E) (L ⊃ ∼Q) • (H ⊃ ∼Q) 2, 3, Conj 
A) (Q ⊃ H) ⊃ L 1, Exp 
B) L ⊃ (H • L) 1, 3, HS 
C) Q ⊃ ∼Q 1, 3, HS 
D) H ⊃ L 2, 3, HS 
E) (L ⊃ ∼Q) • (H ⊃ ∼Q) 2, 3, Conj

Question 19

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, DM 
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, DM

Question 20

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, Trans 
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, Trans

Given the following premises: 1.(C • ∼F) ⊃ E 2.G ∨ (C • ∼F) 3.∼(C • ∼F)

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

Use conditional proof: 1.N ⊃ (F • A) 2.B ⊃ (R • F)/ (N ∨ B) ⊃ (A∨ R)

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

Given the following premises: 1)Q ⊃ (∼N ∨ ∼N) 2)∼N ⊃ ∼∼P 3)P ⊃ ∼G

Use natural deduction to prove the following logical truth: [F • (D ⊃ ∼F)] ⊃ (D ⊃ A)

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

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

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

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

Given the following premises: 1)(E ⊃ K) ∨ W 2)∼W 3)W ∨ ∼(Q ⊃ E)

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

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

Given the following premises: 1)(S • ∼J) ∨ (∼S • ∼∼J) 2)S ∨ ∼S 3)∼J ⊃ P

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

Given the following premises: 1)∼R ≡ ˜R 2)N • ˜T 3)R ⊃ ˜(N • ˜T)

Use an ordinary proof (not conditional or indirect proof): 1.S ⊃ (K • F) 2.F ⊃ (G • H)/ S ⊃ H

Given the following premises: 1)Q ⊃ (H • L) 2)H ⊃ ∼Q 3)L ⊃ ∼Q

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

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

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Exam 7: Natural Deduction in Propositional Logic