Explain why the following are not a complete system of residues modulo 11:
(a) $\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10 \}$
(b) $\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,11, 12 \}$
(c) $\{0, 2, 4, 6, 8, 10, 12, 13, 14, 15, 16 \}$
(a) The set is missing zero, and so is not a complete system of residues modulo 11.
(b) There is a repetition with $0 \equiv 11$ and $1 \equiv 12$ modulo 11.
(c) There is repetition with $2 \equiv 13$ modulo 11, and $4 \equiv 15$. The set is also missing 7 and 9.