Consider the set

$$

$=$

$\{$

$$

$$

$$

$,$

MON,TUE,WED,THU,FRI,SAT

$\}$

$.$

$$Let

$$

$$be a function

$$

:

$$

$->$

$$

$$by

$$

$($

$$

$)$

$=$

$"$the number of elements in

$$

$$that share a letter with

$$

$,$

$$not including itself."

$($

For example, we would not say SUN shares a letter with SUN.

$)$

$[$

$7$

$$points

$]$

Draw an undirected edge

$-$

vertex graph representing which elements share a letter.

What is the largest set of numbers could

$$

$$be for

$$

$$to be an onto function?