Exam 7: Natural Deduction in Propositional Logic

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

Given the following premises: 1)R ⊃ (∼B ⊃ F) 2)∼U ⊃ B 3)∼B

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

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

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

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

Use an ordinary proof (not conditional or indirect proof): 1.K ∨ (S • N) 2.∼(K • ∼Q) 3.∼(N • ∼Q)/ Q

Given the following premises: 1)A 2)G ⊃ (A ⊃ ∼L) 3)∼A ∨ ∼G

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

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

Given the following premises: 1)P ⊃ L 2)∼(J • O) 3)(L ⊃ A) ⊃ (J • O)

Given the following premises: 1)(S ⊃ R) ⊃ (J ⊃ T) 2)(P ⊃ R) ⊃ (S ⊃ R) 3)R ⊃ J

Given the following premises: 1)E ⊃ (B • J) 2)(J • B) ⊃ ∼L 3)L

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

Given the following premises: 1)∼U ⊃ (S • K) 2)R ⊃ (∼U • ∼U) 3)S ≡ ∼U

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

Use conditional proof: 1.G ⊃ (E ⊃ N) 2.H ⊃ (∼N ⊃ E)/ G ⊃ (H ⊃ N)

Given the following premises: 1)T ⊃ (G ∨ G) 2)∼P ⊃ T 3)F ⊃ (B ⊃ ∼P)

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

Given the following premises: 1)D ⊃ H 2)∼D 3)˜(D • S)