Let $G = (V,E)$ be a simple and an undirected graph. Define a relation $R$ on the vertices of $G$ as follows: for two nodes $u$ and $v$, $(u,v) \in R$ if and only if there is a path from $u$ to $v$ in $G$.
a. Determine if $R$ is reflexive, symmetric, anti-symmetric, transitive or total.
b. Why is $R$ an equivalence relation?
c. Suppose $G$ is the graph below. What are the equivalence classes of $R$?