document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1179822>Question 1179822</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find all relations from {4, 5, 6} to {1, 2}.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850167 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(2264)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=850167\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To find all relations from {4, 5, 6} to {1, 2}, we need to find all possible subsets of the Cartesian product of the two sets.\r<BR>\n" );
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document.write( "**1. Cartesian Product:**\r<BR>\n" );
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document.write( "The Cartesian product A × B of sets A = {4, 5, 6} and B = {1, 2} is:\r<BR>\n" );
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document.write( "A × B = {(4, 1), (4, 2), (5, 1), (5, 2), (6, 1), (6, 2)}\r<BR>\n" );
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document.write( "**2. Number of Relations:**\r<BR>\n" );
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document.write( "The number of relations from A to B is equal to the number of subsets of A × B. Since A × B has 6 elements, there are 2⁶ = 64 possible subsets.\r<BR>\n" );
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document.write( "**3. Listing the Relations:**\r<BR>\n" );
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document.write( "We can't list all 64 relations explicitly, but we can describe them:\r<BR>\n" );
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document.write( "* **Empty Relation:** {} (no pairs)<BR>\n" );
document.write( "* **Relations with 1 pair:**<BR>\n" );
document.write( "    * {(4, 1)}<BR>\n" );
document.write( "    * {(4, 2)}<BR>\n" );
document.write( "    * {(5, 1)}<BR>\n" );
document.write( "    * {(5, 2)}<BR>\n" );
document.write( "    * {(6, 1)}<BR>\n" );
document.write( "    * {(6, 2)}<BR>\n" );
document.write( "* **Relations with 2 pairs:**<BR>\n" );
document.write( "    * {(4, 1), (4, 2)}<BR>\n" );
document.write( "    * {(4, 1), (5, 1)}<BR>\n" );
document.write( "    * {(4, 1), (5, 2)}<BR>\n" );
document.write( "    * ... (and so on)<BR>\n" );
document.write( "* **Relations with 3 pairs:**<BR>\n" );
document.write( "    * {(4, 1), (4, 2), (5, 1)}<BR>\n" );
document.write( "    * ... (and so on)<BR>\n" );
document.write( "* ...<BR>\n" );
document.write( "* **Full Relation:** {(4, 1), (4, 2), (5, 1), (5, 2), (6, 1), (6, 2)}\r<BR>\n" );
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document.write( "**General Representation:**\r<BR>\n" );
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document.write( "Any relation R from A to B is a subset of A × B. We can represent it as:\r<BR>\n" );
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document.write( "R ⊆ {(4, 1), (4, 2), (5, 1), (5, 2), (6, 1), (6, 2)}\r<BR>\n" );
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document.write( "To list them all, you would need to write out every possible combination of these pairs.<BR>\n" );
document.write( " </SPAN>\n" );
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