The set of all -tuples for which is called adefinable subset ofThe set is the universe of structure

Sometimes I think I do not understand what a definable subset is.

Here is anexerciseon definable subset:

Let be the underlying set for structure Suppose that is a definable subset of

Suppose we rearrange the order of the -tuples. Consider the set of all such that is inShow that this set is definable.

Then I say that the the sought formula is as follows:

where and defines

While it may be correct, I feel that there is a simpler formula. What do you think?