Set Class Implementation ADT
Python already has built-in abstract base classes for sets and mutable sets — see the collections.abc module. There's even a recipe in the documentation for implementing an immutable set by inheriting from collections.abc.Set and storing the elements in a list.

Here's how you might extend the recipe to a mutable set:

from collections.abc import MutableSet

class ListBasedMutableSet(MutableSet):
    def __init__(self, iterable=()):
        self.elements = []
        for item in iterable:
            self.add(item)

    def __contains__(self, item):
        return item in self.elements

    def __iter__(self):
        return iter(self.elements)

    def __len__(self):
        return len(self.elements)

    def add(self, item):
        if item not in self.elements:
            self.elements.append(item)

    def discard(self, item):
        try:
            del self.elements[self.elements.index(item)]
        except ValueError:
            pass


It's also worth having a look at the implementation of the abstract base classes in _collections_abc.py.