SOLUTION: I need help finishing this proof. (P . Q) -> (R v S) :. (P -> R) v (Q -> S) 1. (P . Q) -> (R v S)

Question 196029: I need help finishing this proof.
(P . Q) -> (R v S) :. (P -> R) v (Q -> S)
1. (P . Q) -> (R v S)
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

1.  (P . Q) -> (R v S) :. (P -> R) v (Q -> S)
---------------------------------
2.  ~(P . Q) v (R v S)                   1    Material Implication
3.  (~P v ~Q) v (R v S)                  2    De Morgan's Law
4.  ~P v (~Q v R) v S                    3    Association
5.  ~P v (R v ~Q) v S                    4    Commutation
6.  (~P v R) v (~Q v S)                  5    Association
7.  (P -> R) v (Q -> S)                  6    Material Implication

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