document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1113762>Question 1113762</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help on constructing the proof to make the argument valid. The Commas are the breaks. Also,  I don't know if I am doing this right\r<BR>\n" );
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document.write( "9.~~A, B-> ~A, A :. ~B\r<BR>\n" );
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document.write( "My work:\r<BR>\n" );
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document.write( "1.~~A<BR>\n" );
document.write( "2. B->~A<BR>\n" );
document.write( "3. A<BR>\n" );
document.write( "4. :. ~B\r<BR>\n" );
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document.write( "ADD Step 1, 2<BR>\n" );
document.write( "MT Steps 3, 4\r<BR>\n" );
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document.write( "Am I correct? I don't know if I am doing this right? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #728854 by </B><A HREF=/tutors/aboutme.mpl?userid=math_helper><B>math_helper(2461)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_helper><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=math_helper><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=728854\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I need help on constructing the proof to make the argument valid. The Commas are the breaks. Also,  I don't know if I am doing this right\r<BR>\n" );
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document.write( "9.~~A, B-> ~A, A :. ~B\r<BR>\n" );
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document.write( "My work:\r<BR>\n" );
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document.write( "1.~~A<BR>\n" );
document.write( "2. B->~A<BR>\n" );
document.write( "3. A<BR>\n" );
document.write( "4. :. ~B\r<BR>\n" );
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document.write( "ADD Step 1, 2<BR>\n" );
document.write( "MT Steps 3, 4\r<BR>\n" );
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document.write( "Am I correct? I don't know if I am doing this right?\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( "I do not think you can use ADD  1,2.    Disjunction Introduction (aka ADD) works like this:\r\n" );
document.write( "1. Q    \r\n" );
document.write( "2. Q v P     1 ADD   (essentially, if \"Q\"  is true then \"Q or P\"  is true)\r\n" );
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document.write( "Here's how I'd do it,  being careful to use Double Negation introduction because many formal logic texts <BR>\n" );
document.write( "say  \"it is not the case that it is not raining\"  is weaker than \"it is raining\" and therefore treat ~~A as slightly weaker than A.   The two are not directly interchangeable without DN elimination or DN introduction (sigh):\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. ~~A          Premise           \r\n" );
document.write( "2. B-->~A       Premise        \r\n" );
document.write( "3. A            Premise\r\n" );
document.write( "4. ~~A          3  Double Negation (DN) \r\n" );
document.write( "5. ~B           2,4  Modus Tollens (MT)   (Conclusion)\r\n" );
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document.write( "</PRE>\r<BR>\n" );
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document.write( "I used to be very good at formal logic, but I'm rusty.  Another tutor may look at my solution and come up with a better one.   I'm pretty certain about not using 1,2 ADD though.<BR>\n" );
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document.write( "EDIT:  As I was reviewing this, I noticed 3. A is probably one of your proof lines (not a premise).  If so, then the proof can be shortened:\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. ~~A          Premise           \r\n" );
document.write( "2. B-->~A       Premise        \r\n" );
document.write( "3. ~B           1,2  Modus Tollens (MT)   (Conclusion)\r\n" );
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document.write( "</PRE>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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