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Example

Let q subset N x N such that q(x, y) <=> x mod 5 = y mod 5. We have

[0]q	=	{0, 5, 10, 15, 20, 25, ...},
[1]q	=	{1, 6, 11, 16, 21, 26, ...},
[2]q	=	{2, 7, 12, 17, 22, 27, ...},
[3]q	=	{3, 8, 13, 18, 23, 28, ...},
[4]q	=	{4, 9, 14, 19, 24, 29, ...},
[5]q	=	{0, 5, 10, 15, 20, 25, ...},
...

We see that [0]_q union [1]_q union [2]_q union [3]_q union [4]_q = N and that any two of these sets are disjoint.