# You are not allowed to import any modules whatsoever

# Assume a set is represented as a Python list

# Do not modify these

A = [1, 2, 5, 8, 12, 5]

B = [3, 5, 7, 8, 11, 3]

# Define a function that takes in a set, represented as a Python list,

# and returns an equivalent set with all duplicates removed

def simplify(A):

# Provide your code here...

# Testing the simplify function

print "A = ", simplify(A)

print "B = ", simplify(B)

# Expected:

# A = [1, 2, 5, 8, 12]

# B = [3, 5, 7, 8, 11]

print

# Define a function that takes in two sets and returns their union.

# The resulting set should be a Python list with no duplicates

def union(A, B):

# Provide your code here...

# Testing the union function

print "A union B = ", union(A, B)

# Expected:

# A union B = [1, 2, 5, 8, 12, 3, 7, 11]

print

# Define a function that takes in two sets and returns their intersection.

# The resulting set should be a Python list with no duplicates

def intersection(A, B):

# Provide your code here...

# Testing the intersection function

print "A intersection B = ", intersection(A, B)

# Expected:

# A intersection B = [5, 8]

print

# Define a function that takes in two sets, A and B, and returns True

# if A is a subset of B, and False otherwise

def subset(A, B):

# Provide your code here...

# Testing the subset function

print "A subset of B:", subset(A, B)

print "[5, 7, 8] subset of B:", subset([5,7,8], B)

# Expected:

# A subset of B: False

# [5, 7, 8] subset of B: True

print

# Define a function that takes in two sets and returns True

# if they are equal, and False otherwise

def equal(A, B):

# Provide your code here...

# Testing the equal function

print "A == B:", equal(A, B)

print "[1, 2, 3, 4] == [1, 1, 2, 2, 4, 2, 3, 3]:", equal([1, 2, 3, 4],[1,

1, 2, 2, 4, 2, 3, 3])

# Expected:

# A == B: False

# [1, 2, 3, 4] == [1, 1, 2, 2, 4, 2, 3, 3]: True

print

# Define a function that takes in two sets and returns their Cartesian

product

# The result should be represented as a list of tuples, ex: [(1, 1), (1,

2), ...]

def cartesian_product(A, B):

# Provide your code here...

# Testing the cartesian_product function

print "[1] x B =", cartesian_product([1], B)

print "[1, 2] x B =", cartesian_product([1, 2], B)

Checking a Condition on List Elements Many of the exercises in this lab will involve checking whether a certain condition is satisfied for every list element. There is a useful construct, sometimes referred to as a flag, which keeps track of the condition as we are going through the loop. To make use of it, we have been given a list, and we assume the condition is true for every element. We set up the code like this: theList-[...1 # Let's assume the condition we are testing is true flag - True for i in theList: if condition does not hold for i # We found an element that does not meet the condition, we are done flag False break # When we are done with the for-loop, the flag will either be True of False # corresponding to whether the condition is true for all elements of the list. # Since we started with flag true, and the only way to make it false is to # find a list element for which the condition is not true, this means that if # flag is false at this point of the code, we must have found a list element that # does not meet the condition, so the condition can't hold for every element Building up a List Sometimes the solution to a problem is to go through a given list (possibly more than one list), and select only those elements for which a certain condition holds, and make that the result. We set up the code in the following way: inputList = [ result- [] # At the start result is empty for i in inputList ..] if condition holds for i: esult.append(i) # At this point result is made up of only those input elements that met the condition