Given a set of equivalence classes, e.g: { {a, b}, {c}, {d} }, is there a way to use WolframAlpha to get its corresponding equivalence relation, and vice versa?
It is not really clear what sort of output is expected here.
As an equivalence relation on a set is a particular kind of (binary) relation, and in general a relation in a set is a set of ordered pairs, I would expect for output:
{ {a, a}, {a, b}, {b, a}, {b, b}, {c, c}, {d, d} }