document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=505652>Question 505652</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A finite set (Omega) has n elements. Show that if we count the empty set and (Omega) as subsets, there are  2^n subsets of (Omega). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #339954 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=339954\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A finite set (Omega) has n elements. Show that if we count the empty set and (Omega) as subsets, there are 2^n subsets of (Omega).<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Consider a set with n slots for the n elements.<BR>\n" );
document.write( "----<BR>\n" );
document.write( "There are two possibilities for each slot.<BR>\n" );
document.write( "Each element of the set is either in or not in its slot.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "There are 2^n possible possible choices.  So there<BR>\n" );
document.write( "are 2^n different set patterns from \"all elements out<BR>\n" );
document.write( "of their slot\" to \"all elements in their slot\".<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "============= </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );