SOLUTION: I need help completing this proof for my deductive logic class? 1. (O . P)--> Q 2. R --> (Q -->S) 3. O . R (Conclusion) P --> S

Question 237510: I need help completing this proof for my deductive logic class?
1. (O . P)--> Q
2. R --> (Q -->S)
3. O . R (Conclusion) P --> S
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

1.   (O . P) -> Q
2.   R -> (Q -> S)
3.   O . R               / P -> S
-------------------------
4.   O                          3     Simplification
5.   R . O                      3     Commutation
6.   R                          5     Simplification
7.   O -> (P -> Q)              1     Exportation
8.   P -> Q                     7,4   Modus Ponens
9.   Q -> S                     2,6   Modus Ponens
10.  P -> S                     8,9   Hypothetical Syllogism

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