document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=325454>Question 325454</A>: <I><SPAN STYLE=\"word-break: break-all;\"> True or False?<BR>\n" );
document.write( "~(~p -> ~q)_= p -> q<BR>\n" );
document.write( "Please note that the equal sign has 3 bars - not sure how to type that in this equation. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #233042 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=233042\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sim (\sim p \rightarrow \sim q) \equiv \sim (\sim(\sim p) \vee \sim q) \equiv \sim (p \vee \sim q) \equiv \sim p \wedge \sim(\sim q) \equiv \sim p \wedge q\">\r<BR>\n" );
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document.write( "So in short, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sim (\sim p \rightarrow \sim q) \equiv \sim p \wedge q\">\r<BR>\n" );
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document.write( "This means that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sim (\sim p \rightarrow \sim q) \not{\equiv} p \rightarrow q\">\r<BR>\n" );
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document.write( "So the statement is false.\r<BR>\n" );
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document.write( "Notice that if p is false and q is false, then <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sim (\sim p \rightarrow \sim q)\"> is false, but <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE p \rightarrow q\"> is true\r<BR>\n" );
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document.write( "So this shows that the two expressions do not have the same truth values. </SPAN>\n" );
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