Question

Write a Python function cardinality() that takes in three Python set objects, representing sets of between 0 and 50 integers, AA, BB, and UU. Your function should return a single non-negative integer value for the cardinality of the set below. AA and BB are subsets (not necessarily proper) of the universal set UU.

|P(A¯¯¯¯∩B)||P(A¯∩B)|

Note 1: You can copy-paste the code declaring the various visible test cases below. We strongly encourage you to do this to test your code.

Note 2: Your function should take in the sets in the order: AA, BB, UU.

For example:

Test	Result
A = {0, 1, 2} B = {1, 3} U = {0, 1, 2, 3, 4} print(cardinality(A, B, U))	2
A = {0, 2, 5, 10, 11, 12, 15, 16, 19, 23, 24, 30} B = {1, 3, 4, 6, 7, 15, 16, 22, 23, 25, 29} U = set(list(range(0,31))) print(cardinality(A, B, U))	256

Answer 1

def cardinality(A, B, U):
    return 2 ** len(U.difference(A).intersection(B))


# Below code is used to test the code. ignore/remove the code below
A = {0, 1, 2}
B = {1, 3}
U = {0, 1, 2, 3, 4}
print(cardinality(A, B, U))

A = {0, 2, 5, 10, 11, 12, 15, 16, 19, 23, 24, 30}
B = {1, 3, 4, 6, 7, 15, 16, 22, 23, 25, 29}
U = set(list(range(0, 31)))
print(cardinality(A, B, U))