Prompt:

After reading instructions, complete required steps: Design and implement a linked implementation of a set data structure in Python.

Your implementation should have the following methods:

Implement a class called "Node" that represents a single node in the linked set. This class should have a value property to store the node's value, and two properties to store pointers to the next node in the set and the previous node in the set.

Implement a class called "LinkedSet" that represents the set data structure. This class should have a property for storing the first node in the set $($the head of the linked list$)$ and a property for storing the last node in the set $($the tail of the linked list$).$

Implement the following methods in the LinkedSet class:

a$.$ "add$($value$)"-$ Adds a value to the set, only if the value is not already in the set.

b$.$ "remove$($value$)"-$ Removes a value from the set. If the value is not in the set, this method should do nothing.

c$.$ "contains$($value$)"-$ Returns True if the set contains the value, and False otherwise.

d$.$ "union$($other$\_$set$)"-$ Returns a new set that is the union of the current set and the other$\_$set. The union of two sets is a set that contains all the elements of both sets.

e$.$ "intersection$($other$\_$set$)"-$ Returns a new set that is the intersection of the current set and the other$\_$set. The intersection of two sets is a set that contains only the elements that are in both sets.

$4.$ The LinkedSet class should be implemented using linked nodes. Do not use any built$-$in data structures like lists or sets to store the values in the set.

$5.$ Test your implementation by creating several sets and performing various operations on them $($adding elements, removing elements, finding the union and intersection of sets$)$ to ensure that the code is working as expected.