how can I visualize such graph and how can I prove it is the way

Question

So I have few examples of graphs one of which is the following. How can visualize it and prove it is the way it should be visualized?

∀x ∃y(xRy) 

Thanks!

Answer 1

Given a binary relation $R$ on a set $X$, a pair $(X,R)$ is a directed graph with the set $X$ of vertices and the set $R$ of edges. Condition $\forall x \exists y(xRy)$ means that each vertex $x\in X$ has an outdoing edge $(x,y)$ for some $y\in X$. It follows that if $|X|\le \frak c$ (in particular, $X$ is finite) then $(X,R)$ can be visualized as a set of points in plane or space, connected by arrows, such that each point has an outgoing arrow.