document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190253>Question 1190253</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Topics In Contemporary Math\r<BR>\n" );
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document.write( " Arguments\r<BR>\n" );
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document.write( "Use truth tables to determine if each of the following arguments are valid or invalid.\r<BR>\n" );
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document.write( "2) If you are superstitious, then do not walk under a ladder.<BR>\n" );
document.write( "If you do not walk under a ladder, then you are superstitious.<BR>\n" );
document.write( "Therefore, you are superstitious and you do not walk under a ladder.\r<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 #821905 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=821905\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "S = you are superstitious<BR>\n" );
document.write( "W = you walk under a ladder<BR>\n" );
document.write( "~S = you are not superstitious<BR>\n" );
document.write( "~W = you do not walk under a ladder\r<BR>\n" );
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document.write( "Premise 1: S -> ~W<BR>\n" );
document.write( "Premise 2: ~W -> S<BR>\n" );
document.write( "Conclusion: S & ~W\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 ></TD><TD ></TD><TD >Premise 1</TD><TD >Premise 2</TD><TD >Conclusion</TD></tr><tr><TD >S</TD><TD >W</TD><TD >~S</TD><TD >~W</TD><TD >S -> ~W</TD><TD >~W -> ~S</TD><TD >S & ~W</TD></tr><tr><TD >T</TD><TD >T</TD><TD >F</TD><TD >F</TD><TD >F</TD><TD >T</TD><TD >F</TD></tr><tr><TD >T</TD><TD >F</TD><TD >F</TD><TD >T</TD><TD >T</TD><TD >T</TD><TD >T</TD></tr><tr><TD >F</TD><TD >T</TD><TD >T</TD><TD >F</TD><TD ><font color=red>T</font></TD><TD ><font color=red>T</font></TD><TD ><font color=red>F</font></TD></tr><tr><TD >F</TD><TD >F</TD><TD >T</TD><TD >T</TD><TD >T</TD><TD >F</TD><TD >F</TD></tr>\n" );
document.write( "</TABLE>Notes:<ul><li>P -> Q is false when P is false and Q is true, otherwise it's true.</li><li>P & Q is true when both P and Q are true together, otherwise it's false</li><li>Whatever you find in column S, flip it to get ~S, and vice versa. Same goes for W to ~W as well.</li></ul>In the table above, the row marked in red highlights a case when we have all true premises but they lead to a false conclusion.<BR>\n" );
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document.write( "This directly leads to the fact <font color=red>the argument is invalid</font>.<BR>\n" );
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