Given the partition $\{a,b,c\}$ and $\{d,e\},\,$ of the set $S=\{a,b,c,d,e\},\,$ list the ordered pairs in the corresponding equivalence relation.
How can I determine which elements are related to which elements, when no explicit equivalence relation is given? Maybe I'm missing something fairly obvious, but as of now, I'm clueless.
Update: All the comments have been extremely helpful and I understand the problem now.
Which elements are related to which elements?
That is, $a R b$ if and only if there exists a cell (subset) X in the partition such that $a\in X$ and $b \in X$. You will see this is indeed and equivalence relation.
Looking at the cell of the partition given by $\{d, e\}$, we know that $(d, d) \in R, (e, e) \in R, (d, e) \in R, (e, d)\in R$.
But we also know, for example, that $(a, d) \notin R$
I'll let your complete listing the ordered pairs in this equivalence relation R.