I agree with Patrick #1 on **Puzzle 11** (or have the same confusion!). A simpler example: Let \\(A = \\{a, b\\}\\) and \\(\leq_A\\) be only \\(\leq_A = \\{(a, a), (b,b)\\}\\). Let \\( (B, \leq_B)\\) be given by \\(B=\\{1, 2\\}\\) with the usual \\(\leq_B\\). Then \\(f = \\{(a, 1), (b, 2)\\}\\) is trivially monotone, but its inverse \\(g\\) clearly isn't.