document.write( "Question 1089734: Help! I need this badly. Use rules of inference and replacement. Thaaaanks!\r
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Algebra.Com's Answer #704096 by math_helper(2461) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "1.   P—>A                    Premise\r\n" );
document.write( "2.   X—>B                    Premise\r\n" );
document.write( "3.   (P v X) —> (A v B)      This follows directly by Constructive Dilemma (CD)\r\n" );
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document.write( "I think this proves it the long way…\r\n" );
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document.write( "1.   P—>A                    Premise\r\n" );
document.write( "2.   X—>B                    Premise\r\n" );
document.write( "3.   P v X                   Premise\r\n" );
document.write( "::4.   P                       Assumption, start Conditional Proof (CP)\r\n" );
document.write( "::5.   A                       4,1 Modus Ponens (MP)\r\n" );
document.write( "::6.   A v B                   5 Addition (ADD)\r\n" );
document.write( "::7.   X                       Assumption\r\n" );
document.write( "::8.    B                      7,2 MP\r\n" );
document.write( "::9.   A v B                   8 ADD          \r\n" );
document.write( "10.  A v B                   1,2,3 Proof By Cases (PBC)  { Discharges CP assumptions }       \r\n" );
document.write( "11.  (P v X) —> (A v B)      1,2  CP\r\n" );
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