SOLUTION: Let A = {0,1,3,4,6,8} List the ordered pairs of relations on A: D={(x,y)|x/3 and y/3 have the same remainder}

Find all the remainders of all members of A when divided by 3:

  0
3)0
  0
  0  <--- 0/3 leaves remainder 0

  0
3)1
  0
  1  <--- 1/3 leaves remainder 1

  1
3)3
  3
  0  <--- 3/3 leaves remainder 0

  1
3)4
  3
  1  <--- 4/3 leaves remainder 1

  2
3)6
  6
  0  <--- 6/3 leaves remainder 0

  2
3)8
  6
  2  <--- 8/3 leaves remainder 2

0/3,  3/3, and 6/3 leave the same remainder 0

1/3 and 4/3 leave the same remainder 1

And of course, every number leaves the same
remainder when divided by 3 as that number ITSELF
leaves when divided by 3.  For instance 8/3 leaves
the same remainder as 8/3 leaves, which is 2.

So D = { (0,0), (0,3), (0,6), (3,0), (6,0),
         (1,1), (1,4), (4,1),
         (8,8) }

Edwin