document.write( "Question 1205226: Use natural deduction to derive the conclusion in each problem.\r
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Algebra.Com's Answer #842197 by math_helper(2461) $\"\"$ $\"About$

You can put this solution on YOUR website!


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document.write( "1.  (P --> Q) ==  P --> (Q v ~P) \r
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document.write( "// Note to prove A == B, need to show A --> B and  B --> A
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document.write( "// Also note I'm using simplified notation as it is easier to enter\r
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document.write( "2. :: P                                Conditional Proof (CP) assumption #1
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document.write( "3. :: Q                                2,1   Modus Ponens (MP)
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document.write( "4. :: Q v ~P                           3     Addition (ADD) 
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document.write( "5. :: P --> (Q v ~P)                   2-4  CP
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document.write( "6. :: (P --> Q) --> (P --> (Q v ~P))   1-5  CP\r
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document.write( "// Now go the other way
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document.write( "7. :: P --> (Q v ~P)                   CP assumption #2
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document.write( "8. :: P                                CP assumption #3
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document.write( "9. :: (Q v ~P)                         8,7 MP
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document.write( "10.:: P --> Q                          9   Material Implication (MI)
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document.write( "11.:: (P --> (Q v ~P)) -->  (P --> Q)  7-10  CP
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document.write( "12.:: (P --> Q) == (P --> (Q v ~P))    6,11  Material Equivalence (ME)
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document.write( "13.(P --> Q) == (P --> (Q v ~P))       2-12  CP\r
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document.write( "There may be shorter ways to go, but this is what came to mind.   \n" );
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