$(20$ points$)$ a$)$ Draw a diagram of a simple graph $G$ that has three components: one with six

vertices, one with four vertices, and one with two vertices. Label all vertices on the graph.

For the remaining parts of the problem, consider the equivalence relation on the vertices of $G$

defined by: uRv if and only if $u$ is connected to $v.$

b$)$ State $($as sets$)$ all the equivalence classes of $R.$

c$)$ Take the largest equivalence class and draw an induced subgraph of $G$ with these

vertices.