$.$ In the class sessions, the notion graphs and related terminologies has been introduced. In this question you are required to provide an understanding of trees and proceed to give your own examples. Answer the following questions:

$($a$)$ What do you understand by the term tree in graph theory?

$(2$ marks$)$

$($b$)$ Give two examples of a graph that is not a tree.

$(4$ marks$)$

$($c$)$ Give two examples of a rooted tree.

$(4$ marks$)$