document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=263743>Question 263743</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given p is true, q is false, and r is true, find the truth value of the statement (~p ^ q) &#8596;  ~r. \r<BR>\n" );
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document.write( "its true.<BR>\n" );
document.write( "i made a truth table but i think im wrong </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #194336 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=194336\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If p is true, then ~p is false (since ~p is the opposite of p).\r<BR>\n" );
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document.write( "Remember that \"^\" means \"and\". The statement p ^ q is only true if BOTH p AND q are true (hence the \"and\"). Since ~p is false, we automatically know that ~p ^ q is false (q doesn't have to be factored in at all).\r<BR>\n" );
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document.write( "Finally, remember that p <-> q is only true if the truth values for p and q are the same. So if p and q are both true, or both false, then p <-> q is true. Think of this as an \"equals\" (ie p = q). Because r is true, ~r is false. Since ~p ^ q is false as well, ~p ^ q and ~r have the same truth values. So (~p ^ q) <-> ~r is true. So you are correct. Good job.\r<BR>\n" );
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document.write( "Here's one way you could write all this out:\r<BR>\n" );
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document.write( "(~p ^ q) <-> ~r\r<BR>\n" );
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document.write( "(~T ^ F) <-> ~T\r<BR>\n" );
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document.write( "(F ^ F) <-> F\r<BR>\n" );
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document.write( "F <-> F\r<BR>\n" );
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document.write( "T\r<BR>\n" );
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document.write( " </SPAN>\n" );
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