document.write( "Question 201425: Hello, I need help with these proofs. I believe they are propositional logic and require rules 1-13 involving everything from Modus Ponens to Double Negation. \r
\n" ); document.write( "\n" ); document.write( "1. Gv(R&E)
\n" ); document.write( "2. (GvE)>~R
\n" ); document.write( "conclusion: GvM\r
\n" ); document.write( "\n" ); document.write( "using rules of replacement and inference. \n" ); document.write( "

Algebra.Com's Answer #151647 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
Here's one way to do it:\r
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document.write( "1.   G v (R & E)\r\n" );
document.write( "2.   (G v E) -> ~R              :.  G v M\r\n" );
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document.write( "3.   (G v R) & (G v E)              1      Distribution\r\n" );
document.write( "4.   (G v E) & (G v R)              3      Commutation\r\n" );
document.write( "5.   G v R                          3      Simplification\r\n" );
document.write( "6.   G v E                          4      Simplification\r\n" );
document.write( "7.   ~R                           2,6      Modus Ponens\r\n" );
document.write( "8.   ~~G v R                        5      Double Negation\r\n" );
document.write( "9.   ~G -> R                        8      Material Implication\r\n" );
document.write( "10.  G                            9,7      Modus Tollens\r\n" );
document.write( "11.  G v M                         10      Addition\r\n" );
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