document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1151809>Question 1151809</A>: <I><SPAN STYLE=\"word-break: break-all;\"> using truth tables, decide if each argument is valid. \r<BR>\n" );
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document.write( "p ∨ ∼q<BR>\n" );
document.write( "∼q → p<BR>\n" );
document.write( "∴ p\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #773679 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=773679\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "premise1 = p v ~q<BR>\n" );
document.write( "premise2 = ~q -> p<BR>\n" );
document.write( "conclusion = p\r<BR>\n" );
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document.write( "p is some logical statement that can be either true (T) or false (F)<BR>\n" );
document.write( "q is also either T or F<BR>\n" );
document.write( "The first two columns of the table below represent the four possible ways to have a T and F combo\r<BR>\n" );
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document.write( "The third column ~q represents the negation of column q. This is the opposite of the q column.\r<BR>\n" );
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document.write( "The fourth column has p and ~q in a disjunction. A disjunction is only false when both parts are false; otherwise, it is true.\r<BR>\n" );
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document.write( "The ~q -> p column is only false when ~q is true while p is false, ie in the form T -> F; otherwise it is true.\r<BR>\n" );
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document.write( "The last column is just a copy of the first column. It's to help set up the conclusion which is often the last column.\r<BR>\n" );
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document.write( "Truth Table<BR>\n" );
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document.write( "<tr><TD >p</TD><TD >q</TD><TD >~q</TD><TD >p v ~q</TD><TD >~q -> p</TD><TD >p</TD></tr>\r\n" );
document.write( "<tr><TD >T</TD><TD >T</TD><TD >F</TD><TD >T</TD><TD >T</TD><TD >T</TD></tr>\r\n" );
document.write( "<tr><TD >T</TD><TD >F</TD><TD >T</TD><TD >T</TD><TD >T</TD><TD >T</TD></tr>\r\n" );
document.write( "<tr><TD >F</TD><TD >T</TD><TD >F</TD><TD >F</TD><TD >T</TD><TD >F</TD></tr>\r\n" );
document.write( "<tr><TD >F</TD><TD >F</TD><TD >T</TD><TD >T</TD><TD >F</TD><TD >F</TD></tr>\r\n" );
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document.write( "</TABLE><BR>\n" );
document.write( "An invalid argument would be if all the premises were true and they lead to a false conclusion. That doesn't happen here because the first two rows have a true conclusion while the last two rows have not all premises being true.\r<BR>\n" );
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document.write( "<font color=red size=4>So the argument is valid.</font><BR>\n" );
document.write( "</font> </SPAN>\n" );
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