On **Puzzle 32**

It seems that they define partition as a pair of some set **P** and family of sets indexed by **P** satisfying some conditions. The set **P** is not defined uniquely. A partition with **n** parts may be defined by *any* set of cardinatlity **n**, whereas an equivalence relation is defined uniquely as a subset of Cartesian product.

It seems that they define partition as a pair of some set **P** and family of sets indexed by **P** satisfying some conditions. The set **P** is not defined uniquely. A partition with **n** parts may be defined by *any* set of cardinatlity **n**, whereas an equivalence relation is defined uniquely as a subset of Cartesian product.