Practice Set 4.3

Proofs for Practice Set 4.3

(1) 1. F ∨ F A Deduce: F


(2) 1. ~A ⊃ B A
2. C ⊃ ~D A
3. ~A ∨ C A Deduce: B ∨ ~D


(3) 1. (H ∨ ~B) ⊃ R A
2. (H ∨ ~M) ⊃ P A
3. H A Deduce: P · R


(4) 1. (D ⊃ B) · (C ⊃ D) A
2. (B ⊃ D) · (E ⊃ C) A
3. B ∨ E A Deduce: D ∨ B


(5) 1. D ∨ (E ∨ G) A Deduce: E ∨ (D ∨ G)


(6) 1. T ∨ (P · ~S) A
2. ~S ⊃ T A
3. ~P ⊃ ~T A Deduce: P ≡ T


(7) 1. D ⊃ (B ≡ A) A
2. D ∨ C A
3. ~A ⊃ ~C A Deduce: B ⊃ A