document.write( "Question 1183507: F → (O • B), S ↔ ~B, , W ↔ ~S, therefore F → W
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Algebra.Com's Answer #813863 by math_helper(2461) $\"\"$ $\"About$

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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.\r
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document.write( "1.  F → (O • B)    Premise
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document.write( "2.  S ↔ ~B         Premise
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document.write( "3.  W ↔ ~S         Premise
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document.write( "// therefore F → W
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document.write( "4.:: F             Conditional Proof (CP) assumption
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document.write( "5.:: O • B         4,1 Modus Ponens (MP)
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document.write( "6.:: B             5  Simplification (SIMP)
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document.write( "7.:: S --> ~B      2  Biconditional elimination
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document.write( "8.:: ~S            6,7  Modus Tollens (MT)
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document.write( "9 :: ~S --> W      3  Biconditional elimination
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document.write( "10.:: W            8,9 MP
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document.write( "11.:: F --> W      4-10 CP
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document.write( "12. F --> W        4-11 CP (discharges CP assumptions)\r
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document.write( "Proof complete\r
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