5 3 1 Set Operations Explained

Key Concepts

Set operations in Python allow you to manipulate sets, which are unordered collections of unique items. The key concepts include:

• Union
• Intersection
• Difference
• Symmetric Difference
• Subset and Superset

1. Union

The union of two sets is a set that contains all the elements from both sets, without duplicates. The union operation is performed using the | operator or the union() method.

Example:

set1 = {1, 2, 3}
set2 = {3, 4, 5}
union_set = set1 | set2
print(union_set)  # Output: {1, 2, 3, 4, 5}
    

Analogy: Think of the union as combining two shopping lists into one, ensuring no duplicate items.

2. Intersection

The intersection of two sets is a set that contains only the elements that are present in both sets. The intersection operation is performed using the & operator or the intersection() method.

Example:

set1 = {1, 2, 3}
set2 = {3, 4, 5}
intersection_set = set1 & set2
print(intersection_set)  # Output: {3}
    

Analogy: Think of the intersection as finding common items between two shopping lists.

3. Difference

The difference between two sets is a set that contains elements that are in the first set but not in the second set. The difference operation is performed using the - operator or the difference() method.

Example:

set1 = {1, 2, 3}
set2 = {3, 4, 5}
difference_set = set1 - set2
print(difference_set)  # Output: {1, 2}
    

Analogy: Think of the difference as finding items in one shopping list that are not in the other.

4. Symmetric Difference

The symmetric difference of two sets is a set that contains elements that are in either of the sets but not in both. The symmetric difference operation is performed using the ^ operator or the symmetric_difference() method.

Example:

set1 = {1, 2, 3}
set2 = {3, 4, 5}
symmetric_difference_set = set1 ^ set2
print(symmetric_difference_set)  # Output: {1, 2, 4, 5}
    

Analogy: Think of the symmetric difference as finding items that are unique to each shopping list.

5. Subset and Superset

A set is a subset of another set if all elements of the first set are contained in the second set. A set is a superset of another set if it contains all elements of the second set. These operations are performed using the <= and >= operators or the issubset() and issuperset() methods.

Example:

set1 = {1, 2, 3}
set2 = {1, 2, 3, 4, 5}
is_subset = set1 <= set2
is_superset = set2 >= set1
print(is_subset)  # Output: True
print(is_superset)  # Output: True
    

Analogy: Think of a subset as a smaller shopping list that is fully contained within a larger shopping list.

Putting It All Together

By understanding and using set operations effectively, you can manipulate and compare sets to suit your needs in various programming tasks. These operations are particularly useful for tasks that involve unique data and comparisons.

Example:

set1 = {1, 2, 3}
set2 = {3, 4, 5}
union_set = set1 | set2
intersection_set = set1 & set2
difference_set = set1 - set2
symmetric_difference_set = set1 ^ set2
is_subset = set1 <= set2
is_superset = set2 >= set1

print(union_set)  # Output: {1, 2, 3, 4, 5}
print(intersection_set)  # Output: {3}
print(difference_set)  # Output: {1, 2}
print(symmetric_difference_set)  # Output: {1, 2, 4, 5}
print(is_subset)  # Output: False
print(is_superset)  # Output: False