document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190301>Question 1190301</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Topics In Contemporary Math<BR>\n" );
document.write( "  Modus Ponens and Modus Tollens\r<BR>\n" );
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document.write( "Translate each of the following into symbols, then determine whether or not the argument <BR>\n" );
document.write( "is valid by providing the appropriate name for the argument form.<BR>\n" );
document.write( "3) I studied or I failed the class.<BR>\n" );
document.write( "I did not fail the class.<BR>\n" );
document.write( "Therefore, I studied. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #821910 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=821910\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "S = I studied<BR>\n" );
document.write( "C = I failed the class\r<BR>\n" );
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document.write( "It's tempting to use F to represent \"I failed the class\", but F has a special meaning in logic and it stands for \"false\". So that's why I avoided using F.\r<BR>\n" );
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document.write( "Premise 1: S v C<BR>\n" );
document.write( "Premise 2: ~C<BR>\n" );
document.write( "Conclusion: S\r<BR>\n" );
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document.write( "This argument is <font color=red>valid by disjunctive syllogism</font>.\r<BR>\n" );
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document.write( "If you wanted, you can rewrite premise 1 into ~S -> C which is equivalent to ~C -> S\r<BR>\n" );
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document.write( "From here, you can use <font color=red>modus ponens</font> to go from ~C -> S to S\r<BR>\n" );
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document.write( "In other words, this argument below<BR>\n" );
document.write( "Premise 1: ~C -> S<BR>\n" );
document.write( "Premise 2: ~C<BR>\n" );
document.write( "Conclusion: S<BR>\n" );
document.write( "uses <font color=red>modus ponens</font>\r<BR>\n" );
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document.write( "Meanwhile, this argument<BR>\n" );
document.write( "Premise 1: ~S -> C<BR>\n" );
document.write( "Premise 2: ~C<BR>\n" );
document.write( "Conclusion: S<BR>\n" );
document.write( "uses <font color=red>modus tollens</font>\r<BR>\n" );
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document.write( "So there are a few ways to show that this argument is valid.<BR>\n" );
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document.write( " </SPAN>\n" );
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