document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190080>Question 1190080</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.(N V O) ⊃ (C • D)<BR>\n" );
document.write( "2.(D V K) ⊃ (P V ~C)<BR>\n" );
document.write( "3.(P V G) ⊃ (N • D)<BR>\n" );
document.write( "∴ ~N </SPAN>\n" );
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document.write( "T = true<BR>\n" );
document.write( "F = false\r<BR>\n" );
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document.write( "To see if we have an invalid argument, we have to try to make the conclusion false and all premises true. \r<BR>\n" );
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document.write( "If ~N = F, then N = T\r<BR>\n" );
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document.write( "If N = T, then N v O = T <BR>\n" );
document.write( "To make (N v O) -> (C * D) true, the C*D portion must be true. This breaks down to C = T and D = T.\r<BR>\n" );
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document.write( "Because D = T, we can say D v K = T<BR>\n" );
document.write( "This leads to P v ~C needing to be true<BR>\n" );
document.write( "C = T tells us ~C = F<BR>\n" );
document.write( "So P = T must be the case if we want P v ~C = T\r<BR>\n" );
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document.write( "If P = T, then P v G = T regardless if G is true or false<BR>\n" );
document.write( "The N*D portion is true because both N = T and D = T together. So (P v G) -> (N*D) is true overall.\r<BR>\n" );
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document.write( "In short, if we have the following <BR>\n" );
document.write( "N = T<BR>\n" );
document.write( "C = T<BR>\n" );
document.write( "D = T<BR>\n" );
document.write( "P = T<BR>\n" );
document.write( "then all the premises will be true, but the conclusion ~N would be false.\r<BR>\n" );
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document.write( "Therefore, this argument is invalid. <BR>\n" );
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document.write( " </SPAN>\n" );
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