1. **Stating the problem:** We want to find elements $x,y$ such that $xR!y$ holds but $xR^*y$ does not. 2. **Recall definitions:** - $xR!y$ means: for any $R$-inductive class $u$, if $x \in u$ then $y \in u$. - $xR^*y$ means: $x \in C(R)$ and for any $R$-inductive class $u$, if $x \in u$ then $y \in u$. 3. **Key difference:** The difference between $R!$ and $R^*$ is the requirement $x \in C(R)$ for $R^*$. 4. **Interpretation:** - $R!$ applies to any $x$, regardless of whether $x$ is in $C(R)$. - $R^*$ requires $x$ to be in $C(R)$. 5. **Conclusion:** - If $x \notin C(R)$, then $xR!y$ can hold (since the condition is vacuously true for all $R$-inductive classes containing $x$), but $xR^*y$ cannot hold because $x \notin C(R)$. 6. **Answer:** Elements $x,y$ such that $x \notin C(R)$ and $xR!y$ hold but not $xR^*y$. **Summary:** $$\boxed{\text{All pairs } (x,y) \text{ with } x \notin C(R) \text{ satisfy } xR!y \text{ but not } xR^*y.}$$