Consider the random vector $\begin{pmatrix} X_0\\ X_1\\ X_2 \end{pmatrix}$ with joint cdf $F$.
Consider the random vector $ \begin{pmatrix} Y_3\\ Y_4\\ Y_5 \end{pmatrix}\equiv \begin{pmatrix} X_1-X_0\\ X_2-X_0\\ X_1-X_2 \end{pmatrix}$ with joint cdf $G$.
We say that $X_0, X_1, X_2$ are exchangeable if $$ F(x_0, x_1, x_2)=F(x_{\pi(0)}, x_{\pi(1)}, x_{\pi(2)}) $$ for any permutation of $\{0,1,2\}$ and for any $(x_0, x_1, x_2)\in \mathbb{R}^3$. We say that $Y_3, Y_4, Y_5$ are exchangeable if $$ G(y_3, y_4, y_5)=G(y_{\varphi(3)}, y_{\varphi(4)}, y_{\varphi(5)}) $$ for any permutation of $\{3,4,5\}$ and for any $(y_3, y_4, y_5)\in \mathbb{R}^3$.
Is it true that
(1) If $X_0, X_1, X_2$ is exchangeable then $Y_3, Y_4, Y_5$ are exchangeable?
(2) If $Y_3, Y_4, Y_5$ is exchangeable then $X_0, X_1, X_2$ are exchangeable?