document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190299>Question 1190299</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( "1) Create a truth table to prove that the Law of Disjunctive Syllogism is a valid argument <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #821915 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=821915\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "The law of disjunctive syllogism has an argument of this format<BR>\n" );
document.write( "Premise 1: P v Q<BR>\n" );
document.write( "Premise 2: ~P<BR>\n" );
document.write( "Conclusion: Q\r<BR>\n" );
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document.write( "Truth table:<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD ></TD><TD ></TD><TD >Premise 1</TD><TD >Premise 2</TD><TD >Conclusion</TD></tr><tr><TD >P</TD><TD >Q</TD><TD >P v Q</TD><TD >~P</TD><TD >Q</TD></tr><tr><TD >T</TD><TD >T</TD><TD >T</TD><TD >F</TD><TD >T</TD></tr><tr><TD >T</TD><TD >F</TD><TD >T</TD><TD >F</TD><TD >F</TD></tr><tr><TD >F</TD><TD >T</TD><TD >T</TD><TD >T</TD><TD >T</TD></tr><tr><TD >F</TD><TD >F</TD><TD >F</TD><TD >T</TD><TD >F</TD></tr>\n" );
document.write( "</TABLE>Carefully look through each row. <BR>\n" );
document.write( "Ask yourself: \"For any single row, do I have all true premises but they lead to a false conclusion?\"<BR>\n" );
document.write( "The answer is \"no\" because row 3 comes close, but the true premises lead to a true conclusion.\r<BR>\n" );
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document.write( "Since we don't have all true premises that don't lead to a false conclusion, this means we can't prove the argument is invalid.\r<BR>\n" );
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document.write( "Therefore, the disjunctive syllogism is valid.\r<BR>\n" );
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document.write( "An example of disjunctive syllogism:<BR>\n" );
document.write( "Premise 1: I either ate pizza or I ate Quiznos<BR>\n" );
document.write( "Premise 2: I didn't eat pizza<BR>\n" );
document.write( "Conclusion: I ate Quiznos\r<BR>\n" );
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document.write( "Replace \"I ate pizza\" with P, and \"I ate Quiznos\" with Q to get the argument format mentioned earlier.<BR>\n" );
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