document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1110263>Question 1110263</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Consider the sets A = {x &#8712; Z | x = 6s + 1 for some s &#8712; Z} and B = {x &#8712; Z | x = 3t + 1 for some t &#8712; Z}. Prove the following:\r<BR>\n" );
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document.write( "a: A &#8838; B\r<BR>\n" );
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document.write( "b: ¬(B &#8838; A)\r<BR>\n" );
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document.write( "So sorry I haven't tried anything, but I have no idea where to even begin. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #725303 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=725303\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Do you understand the definitions of the two sets?<br><BR>\n" );
document.write( "Set A contains all integers that are 1 more than a multiple (positive or negative) of 6:  A = {..., -11, -5, 1, 7, 13, ...}<BR>\n" );
document.write( "Set B contains all integers that are 1 more than a multiple (positive or negative0 of 3:  B = {..., -11, -8, -5, -2, 1, 4, 7, 10, 13, ...}<br><BR>\n" );
document.write( "It is easy to see that every element in A is also in B, but not the other way around; that proves that A is a subset of B but B is not a subset of A.<br><BR>\n" );
document.write( "I'm not going to try to do a formal proof....  You can try it if that's what you need.<BR>\n" );
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