document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=569118>Question 569118</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given p is false, q is true, and r is true, find the truth value of the statement (p V ~q) &#8596;  ~r.\r<BR>\n" );
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document.write( "What in the world is truth value and how do I prove it? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #367235 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=367235\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A truth value is simply a value that can either be true or false.\r<BR>\n" );
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document.write( "Let's use the truth values given to evaluate the logical expression\r<BR>\n" );
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document.write( "(p V ~q) &#8596; ~r ... Start with the given logical expression\r<BR>\n" );
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document.write( "(F V ~T) &#8596; ~T ... Plug in p = F, q = T, r = T\r<BR>\n" );
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document.write( "(F V F) &#8596; F ... Negate T to get F (since ~T = F)\r<BR>\n" );
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document.write( "F &#8596; F ... Evaluate F v F to get F\r<BR>\n" );
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document.write( "T ... Since both sides are equal, the equivalence is true.\r<BR>\n" );
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document.write( "So the truth value of (p V ~q) &#8596; ~r is T (or True) when p is false, q is true, and r is true\r<BR>\n" );
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document.write( "Notes:\r<BR>\n" );
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document.write( "1) p V q is only false when both p and q are false (otherwise it's true)\r<BR>\n" );
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document.write( "2) p &#8596; q is only true if both p and q are of the same truth value (ie when both are either true at the same time or when both are false at the same time) </SPAN>\n" );
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