Re **puzzle 32**
There is a difference in defining symmetry.
In the lecture: for all \\(x,y \in X\\), \\(x \sim y\\) implies \\(y \sim x.\\)
In the book (definition 1.8): \\(a \sim b\\) iff \\(b \sim a\\), for all \\(a,b \in A\\)
Implication is weaker than *iff*, but to be honest I am not sure if this is the root cause of the problem, as for me they *feel*... *equivalent* in this particular case. :-O