Let vertex sets $V_1$ and $V_2$ be defined by $V_1= \{1, 2, 3\}$ and $V_2 = \{a, b, c \}$. Let $E_1 = \{ \{ 1, 2\}, \{2, 3\} \}$, and let $E_2 = \{ \{a, b\}, \{b, c\} \}$ be the edge sets corresponding to the vertex sets $V_1$ and $V_2$, respectively. Write a function f that is a bijection from $V_1$ to $V_2$.
$a.$ Write your function $f$ as a set of ordered pairs. I have no idea how to solve this, but this is the function I came up with. $f = \{(1, a), (2, b), (3, c)\}$
$b.$ Show that $f$ is a bijection. I believe it is a bijection since it is one-to-one and onto, but how do you show this?
$c.$ Let $V = \{a, b, c, d, e\}$ be a vertex set and $E = \{ \{a,b\}, \{b,c\}, {c,d}, \{d,e\}, \{e,c\} \} $ be the edge set corresponding to $V$. True or False: The pair $(V, E)$ is a tree. I would think it is a tree, so true.