In python, Implement cartesianProduct and accompanying functions in the giving code. The docstrings of each function elaborate on the constraints of each fn. Make sure to test your code.

Python code:

"""

Since elements of Python sets must be immutable,

a Python set cannot contain Python sets.

For example, a powerset cannot be represented using Python sets.

So we will simulate a set using lists.

For example, [[1,2], [1,3]] represents the set {{1,2}, {1,3}}.

This works, since lists do not have the immutability constraint.

"""

def randomSet (n, up):

"""Build a random 'set' of integers.

Be sure to guarantee the key property of a set: no duplicates.

>>> randomSet(4, 10)

[5, 3, 2, 8]

Params:

n (int): # of integers in the set

up (int): upperbound

Returns: (list) random 'set' of n integers between 0 and up, inclusive

"""

pass

def cartesianProduct (A, B):

"""Build the Cartesian product of the two sets A and B.

>>> cartesianProduct ([1,2], [3, 4])

[(1,3), (1,4), (2,3), (2,4)]

Params:

A (list): set of integers, represented internally as a list

B (list): set of integers, represented internally as a list

Returns: (list) Cartesian product AxB,

represented internally as a list of tuples

"""

pass

def printSet (L):

"""Print a 'set', using standard set notation.

To restore the correct interpretation, this function prints the 'set'

in true set notation.

Hint: you can print without adding a newline (see print documentation)

>>> printSet ([1,2,3,4])

{1, 2, 3, 4}

>>> printSet ([[1,2], [1,3]]

{{1,2}, {1,3}}

Params: A (list): set of integers

"""

pass

# an example of a test call

A = randomSet (5, 100)

B = randomSet (5, 100)

print ("The Cartesian product of ")

printSet(A)

print ("and")

printSet(B)

print ("is")

printSet (cartesianProduct (A, B))