document.write( "Question 188933: I cannot solve this: I can use: Transportation, Material Implication, Material Equivalence, Exportation, Tautology, Double Negation, Commutation, Association, Distribution, Demorgan's Theorem, Modus Ponems, Modus Tollens, Hypothetical Syllogism, Conjunstion, Simplification, Addition, Constructive Dilemma, Absorption and Disjuntive Syllogism. \r
\n" ); document.write( "\n" ); document.write( "1. p -> (q & r)
\n" ); document.write( "2. ~t -> (~r v ~s) Therefore: (p & s) -> t\r
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\n" ); document.write( "\n" ); document.write( "I know that you must somehow get:
\n" ); document.write( "~p
\n" ); document.write( "~p v ~s Add
\n" ); document.write( "~(p & s) Demorgans
\n" ); document.write( "~(p & s) v t Addition
\n" ); document.write( "(p & s) -> t Implication OR\r
\n" ); document.write( "\n" ); document.write( "~t -> t
\n" ); document.write( "t v t Implication
\n" ); document.write( "t Tautology
\n" ); document.write( "t v ~(p & s) Addition
\n" ); document.write( "~(p & s) v t Commutation
\n" ); document.write( "(p & s) -> t Implication\r
\n" ); document.write( "\n" ); document.write( "But I cannot get the steps before these. Please help! \n" ); document.write( "
Algebra.Com's Answer #141836 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Note: try to involve every premise (the given lines) to find the conclusion.\r\n" );
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document.write( "1. p -> (q & r)\r\n" );
document.write( "2. ~t -> (~r v ~s) Therefore: (p & s) -> t \r\n" );
document.write( "----------------------------------------------\r\n" );
document.write( "3.  ~~t v (~r v ~s)                          2     Material Implication\r\n" );
document.write( "4.  t v (~r v ~s)                            3     Double Negation\r\n" );
document.write( "5.  (~r v ~s) v t                            4     Commutation\r\n" );
document.write( "6.  ~r v (~s v t)                            5     Association\r\n" );
document.write( "7.  ~r v (s -> t)                            6     Material Implication\r\n" );
document.write( "8.  r -> (s -> t)                            7     Material Implication\r\n" );
document.write( "9. ~p v (q & r)                              1     Material Implication\r\n" );
document.write( "10. (~p v q) & (~p v r)                      9     Distribution\r\n" );
document.write( "11. (~p v r) & (~p v q)                      10    Commutation\r\n" );
document.write( "12. ~p v r                                   11    Simplification\r\n" );
document.write( "13. p -> r                                   12    Material Implication\r\n" );
document.write( "14. p -> (s -> t)                            13,8  Hypothetical Syllogism\r\n" );
document.write( "15. (p & s) -> t                             14    Exportation\r\n" );
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