document.write( "Question 188805: 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
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Algebra.Com's Answer #141610 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "1. p <--> q\r\n" );
document.write( "2. p -> r\r\n" );
document.write( "3. p -> (r -> s) Therefore: q -> s\r\n" );
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document.write( "4.  (p -> q) & (q -> p)                      3     Material Equivalence\r\n" );
document.write( "5.  (q -> p) & (p -> q)                      4     Commutation\r\n" );
document.write( "6.  q -> p                                   5     Simplification\r\n" );
document.write( "7.  q -> r                                   6,2   Hypothetical Syllogism\r\n" );
document.write( "8.  q -> (r -> s)                            6,3   Hypothetical Syllogism\r\n" );
document.write( "9.  (q & r) -> s                             8     Exportation\r\n" );
document.write( "10. ~(q & r) v s                             9     Material Implication    \r\n" );
document.write( "11. (~q v ~r) v s                            10    DeMorgan's Theorem\r\n" );
document.write( "12. ~q v (~r v s)                            11    Association\r\n" );
document.write( "13. ~q v (s v ~r)                            12    Commutation\r\n" );
document.write( "14. (~q v s) v ~r                            13    Association\r\n" );
document.write( "15. (q -> s) v ~r                            14    Material Implication\r\n" );
document.write( "16. ~r v (q -> s)                            15    Commutation\r\n" );
document.write( "17. r -> (q -> s)                            16    Material Implication\r\n" );
document.write( "18. q -> (q -> s)                            7,17  Hypothetical Syllogism\r\n" );
document.write( "19. (q & q) -> s                             18    Exportation\r\n" );
document.write( "20. q -> s                                   19    Tautology\r\n" );
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