Introduction to Logic Use all the rules of inference (eight implication rules and ten replacement rules) to complete the proofs. Provide the justification for each step that you derive.[18] 1. ∼ (P ⋅ Q) 2. (P ⋅ Q) ν (R ⋅ S) / Q ν S[20] 1. T ν S 2. ∼ T 3. (S ν S) ⊃ (∼ P ν R) / ∼ R ⊃ ∼ P[22] 1. (∼ P ν Q) ⊃ R 2. (S ν R) ⊃ P 3. P ⊃ Q / Q[24] 1. ∼ Q 2. R ⊃ Q 3. ∼ S ⊃ M 4. R ν (S ⊃ Q) / M ν K[28] 1. P ⊃ (Q ν R) 2. (S ν T) ⊃ R 3. ∼ Q ⋅ ∼ R / ∼ P ⋅ ∼ (S ν T)[32] 1. ∼ P ⊃ (Q ν R) 2. (S ν Q) ⊃ R 3. ∼ R / P[34] 1. C ⊃ F 2. A ⊃ B 3. ∼ F ⋅ A 4. ∼ C ⊃ (B ⊃ D ) / B ⋅ D[38] 1. P ⊃ (R ν S ) 2. ∼ [ (∼ P ν ∼ Q) ν (R ν ∼ L) ] / S
Introduction to Logic Use all the rules of inference (eight implication rules and ten replacement rules) to complete the proofs. Provide the justification for each step that you derive. [18]
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