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
