document.write( "Question 983887: (G&H)>(J<>L)
\n" ); document.write( "G<>H
\n" ); document.write( "(H&~L)v(H&K)
\n" ); document.write( "Conclusion: J>K\r
\n" ); document.write( "\n" ); document.write( "Can somebody please help me with this proof? I know I can use a conditional proof and assume J, but I'm stuck after that! \n" ); document.write( "
Algebra.Com's Answer #604694 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "1. (G&H)>(J<>L)\r\n" );
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document.write( "2.  G<>H\r\n" );
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document.write( "3.  (H&~L)v(H&K)\r\n" );
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document.write( "Conclusion: J>K \r\n" );
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document.write( "----------------------------\r\n" );
document.write( "Using a conditional proof, we assume the truth of J, \r\n" );
document.write( "so we put a \"t\" over all J's\r\n" );
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document.write( "           t\r\n" );
document.write( "1.  (G&H)>(J<>L)\r\n" );
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document.write( "2.  G<>H\r\n" );
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document.write( "3.  (H&~L)v(H&K)\r\n" );
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document.write( "            t \r\n" );
document.write( "Conclusion: J>K \r\n" );
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document.write( "---------------------\r\n" );
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document.write( "Since J<>L appears in 1, and J is t, then we must put a t above all Ls\r\n" );
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document.write( "---------------------\r\n" );
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document.write( "           t  t\r\n" );
document.write( "1.  (G&H)>(J<>L)\r\n" );
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document.write( "2.  G<>H\r\n" );
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document.write( "        t\r\n" );
document.write( "3.  (H&~L)v(H&K)\r\n" );
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document.write( "            t \r\n" );
document.write( "Conclusion: J>K \r\n" );
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document.write( "---------------------\r\n" );
document.write( "Since L has a t over it, in the ~L of 3, we put an f over the ~ \r\n" );
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document.write( "           t  t\r\n" );
document.write( "1.  (G&H)>(J<>L)\r\n" );
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document.write( "2.  G<>H\r\n" );
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document.write( "       ft\r\n" );
document.write( "3.  (H&~L)v(H&K)\r\n" );
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document.write( "            t \r\n" );
document.write( "Conclusion: J>K \r\n" );
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document.write( "---------------------\r\n" );
document.write( "Since there is an f over the ~L in 3, there is also an f\r\n" );
document.write( "over the & of (H&~L).\r\n" );
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document.write( "           t  t\r\n" );
document.write( "1.  (G&H)>(J<>L)\r\n" );
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document.write( "2.  G<>H\r\n" );
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document.write( "      fft    \r\n" );
document.write( "3.  (H&~L)v(H&K)\r\n" );
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document.write( "            t \r\n" );
document.write( "Conclusion: J>K \r\n" );
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document.write( "---------------------\r\n" );
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document.write( "Since the left side of 3. (H&~L) has an f over it, the right\r\n" );
document.write( "side must have a t over it, so that 3 will be a true premise,\r\n" );
document.write( "so we put a t over the & of H&K \r\n" );
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document.write( "           t  t\r\n" );
document.write( "1.  (G&H)>(J<>L)\r\n" );
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document.write( "2.  G<>H\r\n" );
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document.write( "      fft t  t \r\n" );
document.write( "3.  (H&~L)v(H&K)\r\n" );
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document.write( "            t \r\n" );
document.write( "Conclusion: J>K \r\n" );
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document.write( "---------------------\r\n" );
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document.write( "Since the & of H&K has a t over it, both H, K must have t's over them.\r\n" );
document.write( "So we put t's over all K's\r\n" );
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document.write( "           t  t\r\n" );
document.write( "1.  (G&H)>(J<>L)\r\n" );
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document.write( "2.  G<>H\r\n" );
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document.write( "      fft t ttt \r\n" );
document.write( "3.  (H&~L)v(H&K)\r\n" );
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document.write( "            t t \r\n" );
document.write( "Conclusion: J>K \r\n" );
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document.write( "---------------------\r\n" );
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document.write( "Therefore the conclusion is valid, because the assumption of the \r\n" );
document.write( "truth of J leads to the truth of K.\r\n" );
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document.write( "Edwin
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