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QUESTION

# 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. 

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.

     1. ∼ (P ⋅ Q)

2. (P ⋅ Q) ν (R ⋅ S)                         / Q ν S

    1. T ν S

2.  ∼ T

3. (S ν S) ⊃ (∼ P ν R)                   / ∼ R ⊃ ∼ P

      1. (∼ P ν Q) ⊃ R

2. (S ν R) ⊃ P

3. P ⊃ Q                              / Q

    1. ∼ Q

2. R ⊃ Q

3. ∼ S ⊃ M

4. R ν (S ⊃ Q)                               / M ν K

     1. P ⊃ (Q ν R)

2. (S ν T) ⊃ R

3. ∼ Q ⋅ ∼ R                              / ∼ P ⋅ ∼ (S ν T)

     1. ∼ P ⊃ (Q ν R)

2. (S ν Q) ⊃ R

3. ∼ R                                      / P

     1. C ⊃ F

2. A ⊃ B

3. ∼ F ⋅ A

4. ∼ C ⊃ (B ⊃ D )                               / B ⋅ D

      1. P ⊃ (R ν S )

2. ∼ [ (∼ P ν ∼ Q) ν (R ν ∼ L) ]                           / S

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