document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1038664>Question 1038664</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have bee having trouble solving these problems and been at it for hours I need help. Anyone's help would be greatly appreciated. I have to prove them. \r<BR>\n" );
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document.write( "Problem #1<BR>\n" );
document.write( "1) (B^A)->D<BR>\n" );
document.write( "2)A<BR>\n" );
document.write( "3) C->~D/~(C^B)<BR>\n" );
document.write( "4) :. (C^B)\r<BR>\n" );
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document.write( "Problem #2<BR>\n" );
document.write( "1) (D^S)^T<BR>\n" );
document.write( "2) [(Sv~F)vZ]->C/C^T<BR>\n" );
document.write( "3) :. C^T\r<BR>\n" );
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document.write( "Problem #3<BR>\n" );
document.write( "1) A->B<BR>\n" );
document.write( "2) D->E<BR>\n" );
document.write( "3) ~(B^E)/ ~Dv~A<BR>\n" );
document.write( "4) :. ~Dv~A\r<BR>\n" );
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document.write( "Problem #4<BR>\n" );
document.write( "1)~[(A^B) v (Cv~R)]<BR>\n" );
document.write( "2) (T^~S)-> (Cv~R)<BR>\n" );
document.write( "3) ~S/~T<BR>\n" );
document.write( "4) ~T\r<BR>\n" );
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document.write( "Problem #5<BR>\n" );
document.write( "1) (~Z^W)->Q<BR>\n" );
document.write( "2) ~Z<BR>\n" );
document.write( "3) R<-> (W^~Q)/~R<BR>\n" );
document.write( "4) ~R </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #653475 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=653475\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "One question per post, please.\r<BR>\n" );
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document.write( "For the first one you need to do a conditional proof.  Note that by DeMorgan, your conclusion is equivalent to ~C or ~B.\r<BR>\n" );
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document.write( "First assume B, then, having been given A, you have B and A, and then you have D by Modus Ponens.  But D is the same as ~~D.  ~~D makes ~C out of statement 3 by Modus Tollens.  And ~C gives you ~C or ~B.\r<BR>\n" );
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document.write( "Second assume ~B which gives you ~C or ~B directly.\r<BR>\n" );
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document.write( "So either way, you get the desired conclusion.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src=\"http://c0rk.blogs.com/gr0undzer0/darwin-fish.jpg\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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