SOLUTION: F → (O • B), S ↔ ~B, , W ↔ ~S, therefore F → W to demonstrate the validity of the argument. Your proof may utilize any of the Rules of Inference or Equivalence Rules giv

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Question 1183507: F → (O • B), S ↔ ~B, , W ↔ ~S, therefore F → W
to demonstrate the validity of the argument. Your proof may utilize any of the Rules of Inference or Equivalence Rules given in Chapter 8.
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
I will show you by way of a conditional proof. In a conditional proof, you make assumptions and see where the premises take you. Only the conclusion(s) of the conditional portion (which are prefixed with ::) can be carried into the main argument. 


1.  F → (O • B)    Premise

2.  S ↔ ~B         Premise

3.  W ↔ ~S         Premise

// therefore F → W

4.:: F             Conditional Proof (CP) assumption

5.:: O • B         4,1 Modus Ponens (MP)

6.:: B             5  Simplification (SIMP)

7.:: S --> ~B      2  Biconditional elimination

8.:: ~S            6,7  Modus Tollens (MT)

9 :: ~S --> W      3  Biconditional elimination

10.:: W            8,9 MP

11.:: F --> W      4-10 CP

12. F --> W        4-11 CP (discharges CP assumptions)



Proof complete