Question 1

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

Question 2

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

Accepted Answer

To prove the argument using conditional

Question 3

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, Simp 
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, Simp

Question 4

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, Exp 
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, Exp

Question 5

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 6

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 7

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, Assoc 
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, Assoc

Question 8

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

Question 10

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 11

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 12

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, Dist 
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, Dist

Question 13

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 14

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 15

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

Question 16

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 17

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, Add 
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, Add

Question 18

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, Exp 
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, Exp

Question 19

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, CD 
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, CD

Question 20

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, MT 
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, MT

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Basic Concepts

Language: Meaning and Definition

Informal Fallacies

Categorical Propositions

Categorical Syllogisms

Propositional Logic

Predicate Logic

Analogy and Legal and Moral Reasoning

Causality and Mills Methods

Probability

Statistical Reasoning

Hypotheticalscientific Reasoning

Science and Superstition

Filters

Exam 7: Natural Deduction in Propositional Logic