Let A = {1, 2, 3, 4, 5, 6, 7}. For each of the following values of r, determine an equivalence relation R on A with |R| = r, or explain why no such relation exists,
(a) r = 6;
(b) r = 7;
(c) r = 8;
(d) r = 9;
(e) r = 11;
(f) r = 22;
(g) r = 23;
(h) r = 30;
(i) r = 31.