document.write( "Question 302702: Derive the conclusion of the following symbolized argumet.\r
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\n" ); document.write( "2. ~S /(T*R)>~A \n" ); document.write( "

Algebra.Com's Answer #217014 by jim_thompson5910(35256) $\"\"$ $\"About$

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document.write( "1.  T -> [(A * R) -> (S v ~A)]\r\n" );
document.write( "2.  ~S                          /(T * R) -> ~A\r\n" );
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document.write( "3.  T -> [~(A * R) v (S v ~A)]                1     Material Implication\r\n" );
document.write( "4.  T -> [(~A v ~R) v (S v ~A)]               3     De Morgan's Law\r\n" );
document.write( "5.  T -> [(~R v ~A) v (~A v S)]               4     Commutation\r\n" );
document.write( "6.  T -> [(~R v (~A v ~A)) v S]               5     Association\r\n" );
document.write( "7.  T -> [(~R v ~A) v S]                      6     Tautology\r\n" );
document.write( "8.  T -> [(~A v ~R) v S]                      7     Commutation\r\n" );
document.write( "9.  T -> [~A v (~R v S)]                      8     Association\r\n" );
document.write( "10. T -> [A -> (~R v S)]                      9     Material Implication\r\n" );
document.write( "11. (T * A) -> (~R v S)                       10    Exportation\r\n" );
document.write( "12. ~(T * A) v (~R v S)                       11    Material Implication\r\n" );
document.write( "13. (~T v ~A) v (~R v S)                      12    De Morgan's Law\r\n" );
document.write( "14. [(~T v ~A) v ~R] v S                      13    Association\r\n" );
document.write( "15. (~T v ~A) v ~R                            14,2  Disjunctive Syllogism\r\n" );
document.write( "16. ~T v (~A v ~R)                            15    Association\r\n" );
document.write( "17. ~T v (~R v ~A)                            16    Commutation\r\n" );
document.write( "18. (~T v ~R) v ~A                            17    Association\r\n" );
document.write( "19. ~(T * R) v ~A                             18    De Morgan's Law\r\n" );
document.write( "20. (T * R) -> ~A                             19    Material Implication\r\n" );
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