document.write( "Question 1078186: Need help writing out this proof using induction and elimination rules.
\n" ); document.write( "(E V B) --> ~D
\n" ); document.write( "S V D
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\n" ); document.write( "goal: S\r
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\n" ); document.write( "\n" ); document.write( "(P ^ ~Q) --> ~(P <-> Q)\r
\n" ); document.write( "\n" ); document.write( "Prove goal without premises \n" ); document.write( "
Algebra.Com's Answer #692688 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "1. (E V B) --> ~D\r\n" );
document.write( "2.  S V D\r\n" );
document.write( "3.  E          /S\r\n" );
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document.write( "4. E V B       3, addition\r\n" );
document.write( "5. ~D          1,4, modus ponens\r\n" );
document.write( "6. D V S       2, commutation\r\n" );
document.write( "7. S           6,5, disjunctive syllogism\r\n" );
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document.write( "-----------------------------\r\n" );
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document.write( "You didn't specify a method, so truth table\r\n" );
document.write( "is as good as any (without premises), since\r\n" );
document.write( "there are only two variables.\r\n" );
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document.write( "(P ^ ~Q) --> ~(P <-> Q)\r\n" );
document.write( " T F FT  T   F T  T  T\r\n" );
document.write( " T T TF  T   T T  F  F\r\n" );
document.write( " F F FT  T   T F  F  T\r\n" );
document.write( " F F TF  T   F F  T  F \r\n" );
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document.write( "It is valid because there are only T's under the -->\r\n" );
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document.write( "Edwin
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