document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199150>Question 1199150</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use direct or indirect truth table method to determine whether the following argument is valid.<BR>\n" );
document.write( "S ≡ (N • H) / S v ~N // S ⊃ H </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #832881 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=832881\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "I'll use the ampersand symbol & in place of the dot.<BR>\n" );
document.write( "So instead of N • H, I'll write N & H.\r<BR>\n" );
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document.write( "I'll use an arrow in place of the horseshoe symbol.\r<BR>\n" );
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document.write( "Refer to this list of truth table rules<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.algebra.com/algebra/homework/Conjunction/truth-table1.lesson\">https://www.algebra.com/algebra/homework/Conjunction/truth-table1.lesson</a><BR>\n" );
document.write( "For example, the first rule mentioned in that link will help us determine the column labeled N & H.\r<BR>\n" );
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document.write( "Here is the truth table for the current logical argument<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD >Premise</TD><TD ></TD><TD >Premise</TD><TD >Conclusion</TD></tr><tr><TD >S</TD><TD >N</TD><TD >H</TD><TD >N & H</TD><TD >S = (N & H)</TD><TD >~N</TD><TD >S v ~N</TD><TD >S --> H</TD></tr><tr><TD >T</TD><TD >T</TD><TD >T</TD><TD >T</TD><TD >T</TD><TD >F</TD><TD >T</TD><TD >T</TD></tr><tr><TD >T</TD><TD >T</TD><TD >F</TD><TD >F</TD><TD >F</TD><TD >F</TD><TD >F</TD><TD >F</TD></tr><tr><TD >T</TD><TD >F</TD><TD >T</TD><TD >F</TD><TD >F</TD><TD >T</TD><TD >T</TD><TD >T</TD></tr><tr><TD >T</TD><TD >F</TD><TD >F</TD><TD >F</TD><TD >F</TD><TD >T</TD><TD >T</TD><TD >F</TD></tr><tr><TD >F</TD><TD >T</TD><TD >T</TD><TD >T</TD><TD >F</TD><TD >F</TD><TD >F</TD><TD >T</TD></tr><tr><TD >F</TD><TD >T</TD><TD >F</TD><TD >F</TD><TD >T</TD><TD >F</TD><TD >T</TD><TD >T</TD></tr><tr><TD >F</TD><TD >F</TD><TD >T</TD><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 >F</TD><TD >T</TD><TD >T</TD><TD >T</TD><TD >T</TD></tr>\n" );
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document.write( "Circle the rows that have a false conclusion.<BR>\n" );
document.write( "This would be row 2 and row 4.<BR>\n" );
document.write( "Now look through the premises for row 2. Ask yourself: \"are all of the premises true for this row?\" The answer is \"no\". Both premises are false here.\r<BR>\n" );
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document.write( "In row 4, the first premise is false while the second premise is true. Therefore we don't have all true premises here either.\r<BR>\n" );
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document.write( "Since we do not have a list of all true premises lead to a false conclusion, we can definitively say <font color=red>this argument is <font size=4><u>valid</u></font></font>.\r<BR>\n" );
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document.write( "An invalid argument is where all true premises lead to a false conclusion.<BR>\n" );
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