document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=981453>Question 981453</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If(~P->Q)->(PvR)is false, what are the truth values of P,Q and R? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #602452 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=602452\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (~P->Q)->(PvR)is false\r<BR>\n" );
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document.write( "So (~P->Q) is true while (PvR) is false. The generic form X->Y is only false if X is true but Y is false.\r<BR>\n" );
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document.write( "Since (PvR) is false this means that both P and R have to be false. Otherwise, (PvR) would be true.\r<BR>\n" );
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document.write( "P is false, so ~P is true.\r<BR>\n" );
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document.write( "~P is true and (~P->Q) is true. So Q has to be true. If Q were false, then (~P->Q) would be false.\r<BR>\n" );
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document.write( "So \r<BR>\n" );
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document.write( "P = false<BR>\n" );
document.write( "Q = true<BR>\n" );
document.write( "R = false </SPAN>\n" );
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