document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=188825>Question 188825</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. p <--> q<BR>\n" );
document.write( "2. p -> r<BR>\n" );
document.write( "3. p -> (r -> s)  Therefore  q -> s\r<BR>\n" );
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document.write( "...so far I've tried this but I got stuck...<BR>\n" );
document.write( "4. (p -> q) & (q ->p) 1 equivalence<BR>\n" );
document.write( "5. p -> q             4 simplification<BR>\n" );
document.write( "6. (q -> p) & (p -> q)4 Commutation<BR>\n" );
document.write( "7.  q -> p            6 simplification<BR>\n" );
document.write( "8.  q -> (r ->s)      7, 3 Hypothetical Syllogism<BR>\n" );
document.write( "9. (q & r) -> s       8 exportation<BR>\n" );
document.write( "10. (r & q) -> s      9 commutation<BR>\n" );
document.write( "11.  p -> (p & r)     2 Absorption\r<BR>\n" );
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document.write( "please help :( </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #141611 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=141611\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's one way to do it...\r<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
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)                      1     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" );
document.write( "</PRE> </SPAN>\n" );
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