Let $A = \{A_1, A_2, A_3, \cdots, A_n\}$ and $B = \{B_1, B_2, B_3,\cdots, B_n\}$. where $A_i\in \mathbb{Z}$ and $B_i\in \mathbb{Z}$.
Say,
$S_{1} = A_1 + A_2 + A_3 + \cdots + A_n = \sum_{i=1}^{n}{A_{i}} \\ S_{2} = B_1 + B_2 + B_3 + \cdots + B_n = \sum_{i=1}^{n}{B_{i}}$
And,
$X_1 = A_1 \oplus A_2 \oplus A_3 \oplus \cdots \oplus A_n = \bigoplus_{i=1}^{n}{A_{i}} \\ X_2 = B_1 \oplus B_2 \oplus B_3 \oplus \cdots \oplus B_n = \bigoplus_{i=1}^{n}{B_{i}}$
Where $\oplus$ is the XOR operator.
If $S_{1} = S_{2}$ and $X_{1}=X_{2}$, does this imply that $A$ and $B$ contain the same set of integers?