284 Logic as a Tool (i) (¬A ∧ B ) → ¬C, C A ∨ ¬B : ND [¬(A ∨ ¬B)] ← use 4(a) [¬(A ∨ ¬B)] use 4(a) → ¬¬B ¬A [¬B] ⊥ B 1 ¬A ∧ B (¬A ∧ B) → ¬C ¬C C ⊥ A ∨ ¬B (k) ¬(A ∨ B ) ND ¬A ∧ ¬B : ¬(A ∨ B) ¬(A ∨ B) ←− using 2(a) −→ ¬A ¬B ¬A ∧ ¬B (m) ¬A ∧ ¬B ND [A ∨ B] (o) A ∧ ¬B ND ¬(A ∨ B ): ¬A ∧ ¬B [A]1 ¬A ⊥ ⊥ ¬(A ∨ B) ¬A ∧ ¬B [B]1 ¬B ⊥ ¬(A → B ): A ∧ ¬B A B [A → B] ⊥ ¬(A → B) A ∧ ¬B ¬B 1