document.write( "Question 1007486: Let A = {0,1,3,4,6,8} List the ordered pairs of relations on A:
\n" ); document.write( "D={(x,y)|x/3 and y/3 have the same remainder} \n" ); document.write( "
Algebra.Com's Answer #634773 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
Let A = {0,1,3,4,6,8} List the ordered pairs of relations on A:
\n" ); document.write( "D={(x,y)|x/3 and y/3 have the same remainder}
\n" ); document.write( "
\r\n" );
document.write( "Find all the remainders of all members of A when divided by 3:\r\n" );
document.write( "\r\n" );
document.write( "  0\r\n" );
document.write( "3)0\r\n" );
document.write( "  0\r\n" );
document.write( "  0  <--- 0/3 leaves remainder 0\r\n" );
document.write( "\r\n" );
document.write( "  0\r\n" );
document.write( "3)1\r\n" );
document.write( "  0\r\n" );
document.write( "  1  <--- 1/3 leaves remainder 1\r\n" );
document.write( "\r\n" );
document.write( "  1\r\n" );
document.write( "3)3\r\n" );
document.write( "  3\r\n" );
document.write( "  0  <--- 3/3 leaves remainder 0\r\n" );
document.write( "\r\n" );
document.write( "  1\r\n" );
document.write( "3)4\r\n" );
document.write( "  3\r\n" );
document.write( "  1  <--- 4/3 leaves remainder 1\r\n" );
document.write( "\r\n" );
document.write( "  2\r\n" );
document.write( "3)6\r\n" );
document.write( "  6\r\n" );
document.write( "  0  <--- 6/3 leaves remainder 0\r\n" );
document.write( "\r\n" );
document.write( "  2\r\n" );
document.write( "3)8\r\n" );
document.write( "  6\r\n" );
document.write( "  2  <--- 8/3 leaves remainder 2\r\n" );
document.write( "\r\n" );
document.write( "0/3,  3/3, and 6/3 leave the same remainder 0\r\n" );
document.write( "\r\n" );
document.write( "1/3 and 4/3 leave the same remainder 1\r\n" );
document.write( "\r\n" );
document.write( "And of course, every number leaves the same\r\n" );
document.write( "remainder when divided by 3 as that number ITSELF\r\n" );
document.write( "leaves when divided by 3.  For instance 8/3 leaves\r\n" );
document.write( "the same remainder as 8/3 leaves, which is 2.\r\n" );
document.write( "\r\n" );
document.write( "So D = { (0,0), (0,3), (0,6), (3,0), (6,0),\r\n" );
document.write( "         (1,1), (1,4), (4,1),\r\n" );
document.write( "         (8,8) }\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );