In my textbook, they provide a graph $H$ and then list examples of the cliques and the independent sets in $H$. $\begin{align*}V(H)&=\{1,2,3,4,5,6,7,8,9\}\\E(H)&=\{12,23,39,98,87,74,41,26,25,56,36,69,68,57\}\end{align*}$
They list the set $\{4\}$ to be both a clique and an independent set. I am having trouble understanding why $\{4\}$ is both a clique and an independent set.
I know that a subset $S$ is a clique provided that any two distinct vertices are adjacent. So, since $\{4\}$ has only vertex, is it vacuously a clique?
I know that a set $S$ is independent provided $G[S]$ is an edgeless graph. I can see clearly how $\{4\}$ is an edgeless graph since it only has one vertex.
So, can a subset be both a clique and an independent set? Is $\{4\}$ both a clique and an independent set?