Set union, intersection and difference

The union of two sets, $A$ and $B$, is a set that contains all the elements present in either $A$ or $B$ without repeating any elements. If an element appears in both sets, it will only appear once in the resulting union set.

In Python, we can use the .union() method or the | operator to perform this operation.

Using the .union() method

development_team = {"Alice", "Bob", "Clara"}
design_team = {"Bob", "Dana", "Ellie"}

# Find the union of the two sets
all_team_members = development_team.union(design_team)

print(all_team_members)

Output:

{'Alice', 'Clara', 'Dana', 'Ellie', 'Bob'}

The union is commutative - A.union(B) == B.union(A) - since we're simply combining all unique elements.

Using the | operator

We can also use the | operator:

frontend_team = {"Eli", "Juan", "Megan"}
backend_team = {"Megan", "Nina", "Paul"}

# Use the | operator to find the union
complete_team = frontend_team | backend_team

print(complete_team)

Output:

{'Paul', 'Eli', 'Nina', 'Megan', 'Juan'}

The | operator is especially readable when combining multiple sets:

development_team = {"Alice", "Bob", "Clara"}
design_team = {"Bob", "Dana", "Ellie"}
product_team = {"Tom", "Alice", "David"}
all_team_members = development_team | design_team | product_team

print(all_team_members)

Output:

{'Dana', 'David', 'Tom', 'Bob', 'Ellie', 'Alice', 'Clara'}

Note that there are no duplicates in the resulting set.

The intersection of two sets, $A$ and $B$, is a set that contains only the elements that are present in both $A$ and $B$, excluding all items that are in only one of the sets.

In Python, we can utilise the .intersection() method or the & operator to perform this operation.

Using the .intersection() method

odd_numbers = {1, 3, 5, 7, 9}
prime_numbers = {2, 3, 5, 7, 11}

# Find the intersection of the two sets
common_numbers = odd_numbers.intersection(prime_numbers)

print(common_numbers)  # Output: {3, 5, 7}

Like union, intersection is commutative - A.intersection(B) == B.intersection(A).

Using the & operator

We can also use the & operator:

team_a = {"Lisa", "Tom", "Harry"}
team_b = {"Tom", "Harry", "Sally"}

# Use the & operator to find the intersection
common_members = team_a & team_b

print(common_members)  # Output: {'Tom', 'Harry'}

The & operator is especially readable when intersecting multiple sets:

math_students = {"Anna", "John", "Sam"}
science_students = {"Sam", "Lily", "Anna"}
literature_students = {"Anna", "Tom", "Sam"}

honor_students = math_students & science_students & literature_students

print(honor_students)  # Output: {'Anna', 'Sam'}

The set difference between two sets, $A$ and $B$, results in a new set containing all the elements that are present in set $A$ but not in set $B$. This operation effectively subtracts set $B$ from set $A$, and the elements that are common in both sets are not included in the result.

In Python, we can perform this operation using the .difference() method or the - operator.

Using the .difference() method

primary_colors = {"red", "blue", "yellow"}
secondary_colors = {"green", "orange", "purple", "red"}

# Find the difference of the two sets
unique_primary_colors = primary_colors.difference(secondary_colors)

print(unique_primary_colors)  # Output: {'yellow', 'blue'}

Using the - operator

We can also use the - operator:

new_hires = {"Jesse", "Victor", "Julie"}
current_employees = {"Julie", "Michael", "Lucas"}

# Use the - operator to find the difference
exclusive_new_hires = new_hires - current_employees

print(exclusive_new_hires)  # Output: {'Victor', 'Jesse'}

Unlike union and intersection, difference is not commutative - A - B gives different results to B - A.