document.write( "Question 1028017: I'm having a hard time constructing a proof for the following argument.\r
\n" ); document.write( "\n" ); document.write( "M&~Q
\n" ); document.write( "M->S
\n" ); document.write( "S->P
\n" ); document.write( "And the goal is ~(P->Q) \n" ); document.write( "
Algebra.Com's Answer #643303 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( " 1.  M&~Q\r\n" );
document.write( " 2.  M->S\r\n" );
document.write( " 3.  S->P    /~(P->Q)\r\n" );
document.write( "\r\n" );
document.write( " 4.  M          1, siomplification\r\n" );
document.write( " 5.  S          2,4, modus ponens\r\n" );
document.write( " 6.  P          3,5, modus ponens\r\n" );
document.write( " 7.  ~Q&M       1, commutation\r\n" );
document.write( " 8.  ~Q         7, simplification\r\n" );
document.write( " 9.  P&~Q       6,8, conjunction of premises\r\n" );
document.write( "10.  ~~P&Q      9, double negation\r\n" );
document.write( "11.  ~(~PvQ)    10, DeMorgan's law\r\n" );
document.write( "12.  ~(P->Q)    11, Material implication\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );