I am not quite sure howto define SET-PARTITION as a language as in Sipser. Is it

$ $ \{ <S,A,B> \mid (A,B) \text{ is partition of } S \text{ and } \sum_{n\in A} n = \sum_{n\in B} n \} \quad \text{ or } \ \{ <S> \mid \text{ there exists a partition } (A,B) \text{ of } S \text{ with } \sum_{n\in A} n = \sum_{n\in B} n\} \quad ? $ $