Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
For the property $x \in S$ and $s \mathrel{R} y$$x \mathrel{R} y$ imply $y \in S$, I would say that $S$ is saturated by $R$. Thus, in your case, saturated by $R^{-1}$ might be an option.
For the property $x \in S$ and $s \mathrel{R} y$ imply $y \in S$, I would say that $S$ is saturated by $R$. Thus, in your case, saturated by $R^{-1}$ might be an option.
For the property $x \in S$ and $x \mathrel{R} y$ imply $y \in S$, I would say that $S$ is saturated by $R$. Thus, in your case, saturated by $R^{-1}$ might be an option.
For the property $x \in S$ and $s \mathrel{R} y$ imply $y \in S$, I would say that $S$ is saturated by $R$. Thus, in your case, saturated by $R^{-1}$ might be an option.
