SOLUTION: Use Indirect proof to solve the following: B ≡ (A • D) ~A ⊃ (~B ⊃ C) / A ∨ C

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Question 1178624: Use Indirect proof to solve the following:
B ≡ (A • D)
~A ⊃ (~B ⊃ C) / A ∨ C
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
1.  B ≡ (A • D)
2.  ~A ⊃ (~B ⊃ C)                  / A ∨ C

              |3.  ~(A ∨ C)      Assumption for Indirect Proof
              |4.  ~A • ~C                           3, DeMorgan's Law
              |5.  ~A                                4, simplification
              |6.  ~B ⊃ C                            2,5, Modus Ponens
              |7.  ~C ⊃ ~~B                          6, transposition
              |8.  ~C ⊃ B                            7, double negation
              |9.  ~C • ~A                           4, transposition
              |10. ~C                                9, simplification
              |11. B                                 8, Mudus Ponens   
              |12. [B ⊃ (A • D)] • [(A • D) ⊃ B]    1, Material Equivalence
              |13. B ⊃ (A • D)                      12, simplification
              |14. A • D                             13,11
              |15. A                                 14, simplification
              |16. A • ~A                            15,5, conjunction   

17. A ∨ C      lines 3--16          Indirect Proof


Edwin
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