Originally Posted by

**novice** The set of the distinct equivalence classes is a partition of the set $\displaystyle X=\{1,2,3,4\}$.

Since a set of equivalence classes is a collection of pairwise disjoint, nonempty subset of $\displaystyle X$ whose union is $\displaystyle X$. None of $\displaystyle \{1,2\}, \{1,2,3\},\{1,2,4\}$, $\displaystyle \{1,2,3,4\}$ are pairwise disjoint subsets of $\displaystyle X$.

I have a hunch that we are to pick only one of those while these are the possible partitions of $\displaystyle X$:

$\displaystyle \{\{1,2\},\{3,4\}\}$

$\displaystyle \{\{1,2,3\},\{4\}\}$<--doubtful

$\displaystyle \{\{1,2,4\},\{3\}\}$<--doubtful

or

$\displaystyle

\{\{1,2,3,4\}\}

$<--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.