The set of the distinct equivalence classes is a partition of the set

.

Since a set of equivalence classes is a collection of pairwise disjoint, nonempty subset of

whose union is

. None of

,

are pairwise disjoint subsets of

.

I have a hunch that we are to pick only one of those while these are the possible partitions of

:

<--doubtful

<--doubtful

or

<--this too is doubtful

I have strong doubt of for those three since they are not pairwise disjoint with Y. There is also another reason for doubt, since Y={3,4} is a fixed subset of X.

I wonder if there is a book that gives clear illustration in this regard.