document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=476252>Question 476252</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 6. Given the following sets, select the statement below that is NOT true.  <BR>\n" );
document.write( "A = {r, i, s, k, e, d}, B = {r, i, s, e}, C = {s, i, r}<BR>\n" );
document.write( "  (Points : 2) <BR>\n" );
document.write( "      B &#8834; A<BR>\n" );
document.write( "      A &#8834; C<BR>\n" );
document.write( "      B &#8838; A<BR>\n" );
document.write( "      C &#8838; A<BR>\n" );
document.write( "      C &#8838; B\r<BR>\n" );
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document.write( "thank you for your help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #326567 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20060)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=326567\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Note the difference between \"subset\" and \"proper subset\".<BR>\n" );
document.write( "&#8838; and &#8834;.  Both symbols require that every member of the set <BR>\n" );
document.write( "on the left of the symbol is also a member of the element on <BR>\n" );
document.write( "the right of the symbol.  However with &#8834;, the set on the left <BR>\n" );
document.write( "cannot contain ALL OF the elements of the set on the right of &#8834;.     <BR>\n" );
document.write( "IOW, &#8838; and &#8834; are the same EXCEPT when the same set is on both<BR>\n" );
document.write( "side of the symbol.  \"A &#8838; A\" is true but \"A &#8834; A\" is false.  \r<BR>\n" );
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document.write( "&#8838; allows (but does not require) that the set on the left of &#8838; <BR>\n" );
document.write( "contain ALL the members of the set on the right of &#8838;.  The <BR>\n" );
document.write( "symbol &#8834; does not allow that the set on the left contain ALL <BR>\n" );
document.write( "the elements of the set on the right of it.  IOW, \r<BR>\n" );
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document.write( "{t,o,p} &#8838; {p,o,t} is true\r<BR>\n" );
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document.write( "but\r<BR>\n" );
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document.write( "{t,o,p} &#8834; {p,o,t} is false\r<BR>\n" );
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document.write( "To put it another way:\r<BR>\n" );
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document.write( "The only \"improper subset\" is the set itself, because it's<BR>\n" );
document.write( "not properly \"sub\" which means \"less than\".\r<BR>\n" );
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document.write( "---------------------------------------------------------\r<BR>\n" );
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document.write( "B &#8834; A\r<BR>\n" );
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document.write( "A = {r, i, s, k, e, d}, B = {r, i, s, e}, C = {s, i, r}\r<BR>\n" );
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document.write( "That is true because every member of of B = {r, i, s, e}<BR>\n" );
document.write( "is also a member of A = {r, i, s, k, e, d} yet B is not<BR>\n" );
document.write( "equal to A.  So B is a PROPER subset of A <BR>\n" );
document.write( " <BR>\n" );
document.write( "----------------------------------------------------------\r<BR>\n" );
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document.write( "A &#8834; C\r<BR>\n" );
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document.write( "A = {r, i, s, k, e, d}, B = {r, i, s, e}, C = {s, i, r}\r<BR>\n" );
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document.write( "That is false because not every member of of <BR>\n" );
document.write( "A = {r, i, s, k, e, d} is a member of C = {s, i, r}, since <BR>\n" );
document.write( "C has no k, e, or d.  So B is a subset of A.\r<BR>\n" );
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document.write( "-----------------------------------------------------------\r<BR>\n" );
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document.write( "B &#8838; A\r<BR>\n" );
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document.write( "A = {r, i, s, k, e, d}, B = {r, i, s, e}, C = {s, i, r}\r<BR>\n" );
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document.write( "That is true because every member of of B = {r, i, s, e}<BR>\n" );
document.write( "is also a member of A = {r, i, s, k, e, d}.  So B is a PROPER <BR>\n" );
document.write( "subset of A.  B doesn't contain ALL of A\r<BR>\n" );
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document.write( "-----------------------------------------------------------\r<BR>\n" );
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document.write( "C &#8838; A\r<BR>\n" );
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document.write( "A = {r, i, s, k, e, d}, B = {r, i, s, e}, C = {s, i, r}\r<BR>\n" );
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document.write( "That is true because every member of of C = {s, i, r}<BR>\n" );
document.write( "is also a member of A = {r, i, s, k, e, d}.  So C is a PROPER <BR>\n" );
document.write( "subset of A.\r<BR>\n" );
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document.write( "-----------------------------------------------------------\r<BR>\n" );
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document.write( "C &#8838; B \r<BR>\n" );
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document.write( "A = {r, i, s, k, e, d}, B = {r, i, s, e}, C = {s, i, r}\r<BR>\n" );
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document.write( "That is true because every member of of C = {s, i, r}<BR>\n" );
document.write( "is also a member of B = {r, i, s, e}. So C is a PROPER subset <BR>\n" );
document.write( "of B.\r<BR>\n" );
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document.write( "----------------------------------------------------------\r<BR>\n" );
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document.write( "So only A &#8834; C of the above statements is false.\r<BR>\n" );
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document.write( "Edwin</pre> </SPAN>\n" );
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