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