document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=498974>Question 498974</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the truth table for ( p&#709;q) &#8594; (p^q)?\r<BR>\n" );
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document.write( "What is the truth table for (p&#8594;q)&#8596; ~ r ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #337371 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=337371\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> here's  your truth tables.<BR>\n" );
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document.write( "the first truth table is for (pvq) -> (p^q)<BR>\n" );
document.write( "you have 2 variables so you need 4 rows (2 * 2).<BR>\n" );
document.write( "all possible conditions are shown in the truth table for the 2 variables.<BR>\n" );
document.write( "(pvq) is true except when both p and q are false (FF).<BR>\n" );
document.write( "all other conditions make it true (TT, TF, FT).<BR>\n" );
document.write( "(p^q) is false except when both p and q are true (TT).<BR>\n" );
document.write( "all other conditions make it false (TF, FT, FF).<BR>\n" );
document.write( "(pvq) -> (p^q) is true except when (pvq) is true and (p^q) is false (TF).<BR>\n" );
document.write( "all other conditions make it true (TT, FT, FF).\r<BR>\n" );
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document.write( "the second truth table is for (p->q) <-> ~r<BR>\n" );
document.write( "you have 3 variables so you need 8 rows (2 * 2 * 2)<BR>\n" );
document.write( "all possible combinations are shown in the truth table for the 3 variables.<BR>\n" );
document.write( "(pvq) -> (p^q) is true except when (pvq) is true and (p^q) is false (TF).<BR>\n" );
document.write( "all other conditions make it true (TT, FT, FF).<BR>\n" );
document.write( "~r is true when r is false and ~r is false when r is true.<BR>\n" );
document.write( "(p->q) <-> ~r is true when the truth tables for (p->q) and ~r are the same TT, FF).<BR>\n" );
document.write( "(p->q) <-> ~r is falser when the truth tables for (p->q) and ~r are not the same (TF, FT).\r<BR>\n" );
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document.write( "in general, this is how the truth tables work.\r<BR>\n" );
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document.write( "A or B is true in all cases except when A and B are false.<BR>\n" );
document.write( "A and B is false in all cases except when A and B are true.<BR>\n" );
document.write( "A implies B is true in all cases except when A is true and B is false.<BR>\n" );
document.write( "A if and only if B is true when A and B agree (either both true or both false) and is false when A and B disagree (one is true and the other is false).<BR>\n" );
document.write( "not A is true if A is false and is false if A is true.\r<BR>\n" );
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document.write( "here's a truth table that shows all the possible combinations.\r<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "           A   B   ~A    A or B    A and B    A implies B    A if and only if B\r\n" );
document.write( "           T   T    F       T         T            T                   T\r\n" );
document.write( "           T   F    F       T         F            F                   F\r\n" );
document.write( "           F   T    T       T         F            T                   F\r\n" );
document.write( "           F   F    T       F         F            T                   T\r\n" );
document.write( "</PRE>\r<BR>\n" );
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