document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=451006>Question 451006</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Give a counterexample to show that each of the following<BR>\n" );
document.write( "generalizations about the set of integers is<BR>\n" );
document.write( "false:<BR>\n" );
document.write( "a. Closure property for division<BR>\n" );
document.write( "b. Distributive property for division over addition<BR>\n" );
document.write( "c. Commutative property for division<BR>\n" );
document.write( "d. Associative property for division<BR>\n" );
document.write( "e. Associative property for subtraction<BR>\n" );
document.write( "f. Commutative property for subtraction\r<BR>\n" );
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document.write( "Thank you!<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #310207 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=310207\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a. -6/5, a division of two integers, does not produce an integer.\r<BR>\n" );
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document.write( "b.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-5+%2B+3%29%2F4+=+-2%2F4+=+-1%2F2 ALIGN=MIDDLE  ALT=\"%28-5+%2B+3%29%2F4+=+-2%2F4+=+-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, not an integer.\r<BR>\n" );
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document.write( "c. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F5%3C%3E5%2F6 ALIGN=MIDDLE  ALT=\"6%2F5%3C%3E5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "d.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Fb%29%2Fc+=+a%2F%28bc%29 ALIGN=MIDDLE  ALT=\"%28a%2Fb%29%2Fc+=+a%2F%28bc%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, while <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2F%28b%2Fc%29+=+%28ac%29%2Fb ALIGN=MIDDLE  ALT=\"a%2F%28b%2Fc%29+=+%28ac%29%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" >, hence <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Fb%29%2Fc+%3C%3Ea%2F%28b%2Fc%29 ALIGN=MIDDLE  ALT=\"%28a%2Fb%29%2Fc+%3C%3Ea%2F%28b%2Fc%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "e.  (1-2)-3 = -1 - 3 = -4, whereas 1-(2-3) = 1--1 = 2.\r<BR>\n" );
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document.write( "f.  4-7 = -3, whereas 7-4 = 3. </SPAN>\n" );
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