In this assignment you will program a few functions that allow a list to have the functionality of a set data structure $($remember list can have duplicates but sets do not so your code should not return duplicate values even if the input list contain duplicates$).$ This includes creating a new set, adding$/$removing elements etc. Complete details are provided in the code template below. We have also $($mostly$)$ implemented two of the functions to give you an idea of what's expected $($set$\_$new$(),$ and set$\_$remove$()).$ All the functions should be just a few lines of code.

In this assignment we will represent sets using the Python list data structure. For example:

s $=[1,\text{'}$a$\text{'},3]$

represents the mathematical set object $\{1,\text{'}$a$\text{'},3\}.$

Note that since order does not matter, the same set can be represented by a list that has the elements of the set in a different order. In your implementation, the result returned by your code should not depend on the order in which the elements appear in the list.

Your job is to implement the following set operations:

def set$\_$new$()$ :

$"""$Return a new set"""

return $[]$

def set$\_$remove$($s$,$ value$)$:

$"""$Remove the given value from the set s$"""$

# perform some type checking to see that the user

# has provided the right kind of input:

if type$($s$)!=$type$([])$ :

raise ValueError

# we can simply use the "remove" method of a list:

s$.$remove$($value$)$

# to be complete before returning we should make sure there are no duplicates $-$ not shown

return s

def set$\_$union$($s$1,$ s$2)$ :

$"""$Return the union of sets s$1$ and s$2$ as a list"""

if type$($s$1)!=$type$([])$ or type$($s$2)!=$type$([])$:

raise ValueError

return

def set$\_$intersection$($s$1,$ s$2)$ :

$"""$Return the intersection of sets s$1$ and s$2$ as a list"""

if type$($s$1)!=$type$([])$ or type$($s$2)!=$type$([])$:

raise ValueError

return

def set$\_$membership$($s$,$ value$)$:

$"""$Return True if value is in the set s$,$ and False otherwise"""

if type$($s$)!=$type$([])$ :

raise ValueError

return

def set$\_$equals$($s$1,$ s$2)$ :

$"""$Return True if the sets s$1$ and s$2$ have exactly the same elements"""

if type$($s$1)!=$type$([])$ or type$($s$2)!=$type$([])$:

raise ValueError

return

def set$\_$difference$($s$1,$ s$2)$ :

$"""$Return the set difference of s$1$ and s$2"""$

if type$($s$1)!=$type$([])$ or type$($s$2)!=$type$([])$:

raise ValueError

return $[]$

def is$\_$subset$($s$1,$ s$2)$ :

$"""$Return True if s$1$ is a subset of s$2"""$

if type$($s$1)!=$type$([])$ or type$($s$2)!=$type$([])$:

raise ValueError

return

def is$\_$proper$\_$subset$($s$1,$ s$2)$ :

$"""$Return True if s$1$ is a proper subset of s$2"""$

if type$($s$1)!=$type$([])$ or type$($s$2)!=$type$([])$:

raise ValueError

return